revision test physics

RESONANCE 1

SINGLE CHOICE QUESTIONS

1. A particle is projected from origin O with a velocity (30 i + 40 j) m/s. Then the position vector of the particle 5seconds later is : (take g = 10 m/s2)(A) 150 i + 200j m (B) 150 i + 75 j m(C) 30i + 75j m (D) Nothing can be predicted.

2. For a particle moving in a straight line, the displacement of the particle at time t is given byS = t3 � 6t2 + 3t + 7

What is the velocity of the particle when its acceleration is zero?(A) � 9 m s�1 (B) � 12 m s�1 (C) 3 m s�1 (D) 42 m s�1

3. The velocity of a particle moving on the x-axis is given by v = x2 + x where v is in m/s and x is in m. Find itsacceleration in m/s2 when passing through the point x = 2m(A) 0 (B) 5 (C) 11 (D) 30

4. A parachutist drops freely from an aeroplane for 10 s before the parachute opens out. Then he descends witha net retardation of 2.5 ms�2. If he bails out of the plane at a height of 2495 m and g = 10 ms�2, his velocity onreaching the ground will be(A) 2.5 ms�1 (B) 7.5 ms�1 (C) 5 ms�1 (D) 10 ms�1

5. A particle can travel from point A to B from two different paths 1 and2, as shown, in same interval of time. Then which of the following isincorrect?(A) Average velocity along the two paths must be equal(B) The particle may travel along both the paths unaccelerated(C) The direction of instantaneous velocity along the path 1 & 2 can be same for a maximum of two

point on the paths.(D) The average and instantaneous velocity along path 1 can have same direction.

6. Two trains, which are moving along different tracks in opposite directions, are put on the same trackdue to a mistake. Their drivers, on noticing the mistake, start slowing down the trains when the trainsare 300 m apart. Graphs given below show their velocities as function of time as the trains slow down.The separation between the trains when both have stopped, is :

(A) 120 m (B) 280 m (C) 60 m (D) 20 m.

REVISION TEST - 01Course : VIJAY (R)

TOPIC : KINEMATICS(1-D & RELATIVE MOTION)

Time : 3 Hrs. Max. Marks : 133

Instructions :1. For each correct single choice question 3 marks (with 1 mark negative making).2. For each correct multiple choice question 4 marks (no negative marking).3. For each correct answer in comprehension 4 marks (with 1 mark negative marking).4. For each match the column question 6 marks (no negative marking).5. For each correct assertion/reason question 3 marks (with 1 mark negative marking).

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RESONANCE 2

7. Position (Km) - Time (min.) graph is shown for two cars �A� and �B�. Both

collide at time t = 150 minute. Then the distance of position �R� of accident

from the starting point �Q� of car A will be. (Initial distance between the two

cars is 500 km) (Position in the graph shows the distance of the two carsfrom the point �Q�) - (A) 200 km (B) 300 km(C) 250 km (D) 400 km

8. A particle starts from rest with uniform acceleration and its velocity after n seconds is v. The displacement ofthe body in last two seconds is

(A) n

)1n(v (B)

n)1n(v2

(C) n

)1n(v2 (D)

n)1n(v

9. A boat is rowed across a river at the rate of 4.5 km/hr. The river flows at the rate of 6 km/hr. The velocityof boat in m/s is:(A) 3.1 (B) 2.1 (C) 2.9 (D) 5

10. An aeroplane is to go along straight line from A to B, and back again. The relative speed with respectto wind is V.. The wind blows perpendicular to line AB with speed . The distance between A and B isl. The total time for the round trip is:

(A) 22V v

2(B) 22

V v

v

2(C) 22

V v

V

2(D) 22

V v

2

11. A man can swim in still water with a speed of 3 m/s. x and y axis are drawnalong and normal to the bank of river flowing to right with a speed of 1 m/s.The man starts swimming from origin O at t = 0 second. Assume size ofman to be negligible. Find the equation of locus of all the possible pointswhere man can reach at t = 1 sec.

V =1m/sriver

flow

y

O

river

x(A) (x � 1)2 + y2 = 3 (B) (x � 1)2 + y2 = 9(C) x2 + (y � 1)2 = 3 (D) x2 + (y � 1)2 = 9

12. P is a point moving with constant speed 10 m/s such that its velocityvector always maintains an angle 60° with line OP as shown in figure (O is

a fixed point in space). The initial distance between O and P is 100 m.After what time shall P reach O.

(A) 10 sec. (B) 15 sec. (C) 20 sec. (D) 20 3 sec

13. During a rainy day, rain is falling vertically with a velocity 2m/s. A boy at rest starts his motion with a constantacceleration of 2m/s2 along a straight road. Find the rate at which the angle of the axis of umbrella withvertical should be changed so that the rain always falls parallel to the axis of the umbrella.

(A) 2t1

1

(B) 2t1

2

(C) 2t2

1

(D) 2t21

1

14. A train is standing on a platform , a man inside a compartment of a train drops a stone . At the same instanttrain starts to move with constant acceleration . The path of the particle as seen by the person who drops thestone is :(A) parabola(B) straight line for sometime & parabola for the remaining time(C) straight line(D) variable path that cannot be defined

15. Two boats A and B having same speed relative to river are moving in a river. Boat A moves normal to theriver current as observed by an observer moving with velocity of river current. Boat B moves normal tothe river as observed by the observer on the ground.(A) To a ground observer boat B moves faster than A(B) To a ground observer boat A moves faster than B(C) To the given moving observer boat B moves faster than A(D) To the given moving observer boat A moves faster than B

RESONANCE 3

16. For four particles A, B, C & D, the velocities of one with respect to other are given as DCV is 20 m/s towards

north, BCV is 20 m/s towards east and BAV is 20 m/s towards south. Then DAV is

(A) 20 m/s towards north (B) 20 m/s towards south(C) 20 m/s towards east (D) 20 m/s towards west

MULTIPLE CHOICE QUESTIONS

17. A particle moves in xy plane in such a way that its distance �r� from the origin depends upon time �t� as r = 3t.

The angle �� made by its position vector with the positive x-axis at any time �t� is given as ; = 2t. Here r isin metres, in rad and t in seconds.(A) The particle moves in circular motion.

(B) At time t = 0.5 s, its speed is 3 2 m/s.(C) At time t = 0.5 s, its velocity vector makes an angle 45° with its position vector at the same time.

(D) At time t = 0.5 s, its velocity vector makes an angle 30° with its position vector at the same time.

18. Two particles, one with constant velocity 50m/s and the other with uniform acceleration 10m/s2, startmoving simultaneously from the same position in the same direction. They will be at a distance of125m from each other after(A) 5 sec. (B) 5(1 + 2) sec. (C) 10sec. (D) 10(2 + 1)sec.

19. A man standing on the edge of the terrace of a high rise building throws a stone vertically up with a speed of20 m/s. Two seconds later an identical stone is thrown vertically downwards with the same speed of 20 m/s.Then:(A) the relative velocity between the two stones remain constant till one hits the ground(B) both will have the same kinetic energy when they hit the ground(C) the time interval between their hitting the ground is 2 seconds(D) if the collisions on the ground are perfectly elastic both will rise to the same height above the ground.

20. A cart with a mass M = 1/2 kg is connected by a string to a weight ofmass m = 200 g. At the initial moment the cart moves to the left alonga horizontal plane at a speed V0 = 7 ms 1. All the surfaces are smooth(g = 9.8 ms 2) (A) the distance covered by cart in 5 s is zero(B) after 5 s weight of mass m will be in same position(C) the distance covered by cart in 5 s is 17.5 m(D) none of the above

21. A particle moves with an initial velocity v0 and retardation v, where v is its velocity at any time t ( is

a positive constant).(A) the particle will cover a total distance of v

0/

(B) the particle will continue to move for a very long time(C) the particle will stop shortly(D) the velocity of particle will become v

0/2 after time 1/.

22. A particle is moving rectilinearly so that its acceleration is given as a = 3t2+1 m/s2.Its initial velocity is zero.(A) The velocity of the particle at t=1 sec will be 2m/s.(B) The displacement of the particle in 1 sec will be 2m.(C) The particle will continue to move in positive direction.(D) The particle will come back to its starting point after some time.

23. A man is standing on a road and observes that rain is falling at angle 45º with the vertical. The man

starts running on the road with constant acceleration 0.5 m/s2. After a certain time from the start of the

motion, it appears to him that rain is still falling at angle 45º with the vertical, with speed 22 m/s .Motion of the man is in the same vertical plane in which the rain is falling. Then which of the followingstatement(s) are true.(A) It is not possible(B) Speed of the rain relative to the ground is 2 m/s.(C) Speed of the man when he finds rain to be falling at angle 45º with the vertical, is 4m/s.

(D) The man has travelled a distance 16m on the road by the time he again finds rain to be falling at angle 45°.

RESONANCE 4

COMPREHENSION

Comprehension - 1

Raindrops are falling with a velocity 10 2 m/s making an angle of 450 with the vertical. The drops appear tobe falling vertically to a man running with constant velocity. The velocity of rain drops change such that the

rain drops now appear to be falling vertically with 3 times the velocity it appeared earlier to the same person

running with same velocity.

24. The magnitude of velocity of man with respect to ground is

(A) 10 2 m/s (B) 10 3 m/s (C) 20 m/s (D) 10 m/s

25. After the velocity of rain drops change, the magnitude of velocity of raindrops with respect to ground is

(A) 20 m/s (B) 20 3 m/s (C) 10 m/s (D) 10 3 m/s

26. The angle (in degrees) between the initial and the final velocity vectors of the raindrops with respect to theground is(A) 8 (B) 15 (C) 22.5 (D) 37

Comprehension - 2A overhead bridge, a subway and a road start from A and again meet at B. The minimum distancebetween A and B, which is same as the length of the road AB, is 2 km. The overbridge and the subwayform a semicircular arc above and below the road. A laser sensor is fixed (embedded) in the road.An Autorickshaw takes the overbridge from A and a taxi takes the subways from B.The laser sensorgives a beep when the linear distances between point A and the autorickshaw is same as that betweenthe rickshaw and the laser sensor which also equals the distance of laser source from point A.

27. If the time t, for the laser starts when the autorickshaw just enters the bridge from point A and at t =240 sec, laser the gives a beep, what is the speed of the autorickshaw ?(A) 4.36 m/s (B) 1.21 m/s (C) 8.16 m/s (D) 16.32 m/s

28. The autorickshaw takes the overhead bridge from A and on reaching B, immediately takes the subwayto come back to A, while the taxi starts from B travels to and fro from B to A continuously by road. If the

auto and the taxi travel with constant speeds of 2

km/hr and 3 km/hr respectively, how frequently do

they meet at A ?

(A) every 4 hours (B) every 3

n2 hours, n = 3,6,9,....

(C) every 32

hours (D) they never meet

29. Due to heavy rains, the flyover and the roads were blocked and all the vehicles had to take the subway.

The autorickshaw and the taxi started from A and B respectively with the speeds 2

and 32

km/hr

respectively. After how much time did they meet ?

(A) 67

hours (B) 76

hours (C) 32

hours (D) 76

hours

RESONANCE 5

Comprehension - 3Mr. Shyam drives his car at uniform speed from bottom of a mountainto the top in 20 minutes along a helical path as shown. At the beginning the speedometer of his car shows 8315 km, whileon reaching the top it reads 8335 km.(Take upward as positive y-axis and positive x-axis towards right)

30. The total distance covered is :

(A) 10 km (B) 20 km (C) 25 km (D) can not be determine

31. His displacement vector during the journey is :

(A) )j�4i�3( km (B) 3 km (C) 5 km (D) none of these

32. The average velocity during the journey is :

(A) )j�12i�9( km/hr (B) )j�3.3i�5.2( m/s (C) (25/8) m/s (D) None of these

MATCH THE COLUMN

33. Two particles A and B moving in x-y plane are at origin at t = 0 sec. The initial velocity vectors of A and

B are Au

= 8 i� m/s and Bu

= 8 j� m/s. The acceleration of A and B are constant and are Aa

= �2 i� m/s2

and Ba

= � 2 j� m/s2. Column gives certain statements regarding particle A and B. Column gives

corresponding results. Match the statements in column with corresponding results in Column .Column I Column II

(A) The time (in seconds) at which velocity (p) 16 2 of A relative to B is zero

(B) The distance (in metres) between A and B (q) 8 2 when their relative velocity is zero.(C) The time (in seconds) after t = 0 sec, (r) 8 at which A and B are at same position(D) The magnitude of relative velocity of A and B (s) 4 at the instant they are at same position.

34. A particle is moving along a straight line. Its velocity varies with time as v = kt, where k is a positive constantand t is the time. Match the graphs in Column with the statements in Column

Column Column

(A) Acceleration versus time curve (p)

(B) Acceleration versus displacement curve (q)

(C) Velocity versus time curve (r)

(D) Displacement versus velocity curve (s)

RESONANCE 6

ASSERTION / REASON

35. Assertion : If acceleration of a particle is decreasing then it is possible that velocity is increasing with time.Reason : Acceleration is rate of change of velocity.(A) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion.(B) If both Assertion and Reason are true, but Reason is not correct explanation of the Assertion.(C) if Assertion is true, but the Reason is false.(D) if Assertion is false, but the Reason is true.

36 STATEMENT�1 : The equation of distance travelled by a particle moving in a straight line with constant

acceleration in nth second is Sn = u + (2n � 1)

2a

, where letters have usual meaning, is dimensionally

incorrect.STATEMENT�2: For every equation relating physical quantities to be true, it must have dimensionalhomogenity.(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1(C) Statement-1 is True, Statement-2 is False(D) Statement-1 is False, Statement-2 is True.

37. STATEMENT-1 : The magnitude of velocity of two boats relative to river is same. Both boats start simultaneouslyfrom same point on one bank may reach opposite bank simultaneously moving along different paths.STATEMENT-2 : For boats to cross the river in same time. The component of their velocity relative to river indirection normal to flow should be same.(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1(C) Statement-1 is True, Statement-2 is False(D) Statement-1 is False, Statement-2 is True

Answer Key (Revision Test - 01)1. (B) 2. (A) 3. (D) 4. (C) 5. (B)6. (D) 7. (B) 8. (C) 9. (B) 10. (A)11. (B) 12. (C) 13. (A) 14. (C) 15. (B)16. (D) 17. (B)(C) 18. (A)(B) 19. (A)(B)(C)(D) 20. (B) (C)21. (A)(B) 22. (A)(C) 23. (C)(D) 24. (D) 25. (A)26. (B) 27. (A) 28. (D) 29. (B) 30. (B)31. (A) 32. (A) 33. (A) s (B) p (C) r (D) q34. (A) p (B) p (C) q (D) r 35. (A) 36 (D) 37. (A)

Solution will be provided with next revision test.

RESONANCE 1


REVISION TEST - 02COURSE : VIJAY (R)

TOPIC : PROJECTILE MOTIONSUBJECT : PHYSICS

Time : 1½ Hrs. Max. Marks : 48

Instructions :1. For each correct single choice question 3 marks (with 1 mark negative making).2. For each correct answer in comprehension 4 marks (with 1 mark negative marking).3. For each match the column question 6 marks (no negative marking).4. For each correct assertion/reason question 3 marks (with 1 mark negative marking).

1. A particle when projected in vertical plane moves along the fixed smooth surfacewith initial velocity 20 m/s at an angle of 60º, so that its normal reaction on the

surface remains zero throughout the motion. Then the slope of the tangent to thesurface at height 5 m from the point of projection A will be:

(A) 30º (B) 45º (C) tan1 2 (D) tan1 2

2. A particle moves along the parabolic path y = ax2 in such a way that the y-component of the velocity remainsconstant, say c. The x and y coordinates are in meters. Then acceleration of the particle at x =1 m is

(A) ac k� (B) 2ac2 j� (C) i�a4

c2

2

(D) i�a2c

3. An object is thrown from a point �A� horizontally from a tower and hits the

ground 3s later at B. The line from �A� to �B� makes an angle of 30º with the

horizontal. The initial velocity of the object is : (take g = 10 m/s2)

(A) 315 m/s (B) 15 m/s

(C) 10 3 m/s (D) 3/25 m/s

4. A particle is projected from a point P (2, 0, 0)m with a velocity 10 m/s making an angle 45º with the

horizontal. The plane of projectile motion passes through a horizontal line PQ which makes an angle of37º with positive x-axis, xy plane is horizontal. The coordinates of the point where the particle will

strike the line PQ is: (Take g = 10 m/s2)(A) (10, 6, 0)m (B) (8, 6, 0)m (C) (10, 8, 0)m (D) (6, 10, 0)m

5. A car starts with constant acceleration a = 2m/s2 at t = 0. Two coins are released from the car att = 3 & t = 4. Each coin takes 1 second to fall on ground. Then the distance between the two coins will be(Assume coin sticks to the ground)(A) 9 m (B) 7 m (C) 15 m (D) 2m

6. Velocity of a stone projected, 2 second before it reaches the maximum height, makes angle 53° with the

horizontal then the velocity at highest point will be(A) 20 m/s (B) 15 m/s (C) 25 m/s (D) 80/3 m/s

7. Two guns are mounted (fixed) on two vertical cliffs that are very high from theground as shown in figure. The muzzle velocity of the shell from G1 is u1 andthat from G2 is u2. The guns aim exactly towards each other The ratio u1 : u2such that the shells collide with each other in air is (Assume that there is noresistance of air)

(A) 1 : 2 (B) 1 : 4(C) will not collide for any ratio (D) will collide for any ratio

8. A stone is projected from level ground such that its horizontal and vertical components of initial velocity areu

x = 10 m/s and u

y = 20 m/s respectively. Then the angle between velocity vector of stone one second before

and one second after it attains maximum height is :(A) 30° (B) 45° (C) 60° (D) 90°

COMPREHENSIONComprehension

A stone is projected from level ground with speed u and at an angle with horizontal. Some how theacceleration due to gravity (g) becomes double (that is 2g) immediately after the stone reaches themaximum height and remains same thereafter. Assume direction of acceleration due to gravity alwaysvertically downwards.


RESONANCE 2

9. The total time of flight of particle is :

(A) gsinu

23

(B) gsinu

2

11 (C) g

sinu2 (D)

2

12

gsinu

10. The horizontal range of particle is

(A) g2sinu

43 2

(B)

2

11

g22sinu2

(C) gu2

sin2 (D)

2

12

g22sinu2

11. The angle which the velocity vector of stone makes with horizontal just before hitting the ground isgiven by :

(A) tan = 2 tan (B) tan = 2 cot (C) tan = 2 tan (D) tan = 2 cot

MATCH THE COLUMN

12. Match the following.The projectile collides perpendicularly with the inclined plane. (Refer the figure)

u

(a) Maximum height attained by the (P) zero projectile from the ground

(b) Maximum height attained by (Q) g the projectile from Inclined plane

(c) Acceleration of the projectile before (R)

cosg2sinu 22

striking the inclined plane

(d) Horizontal component of acceleration of the projectile. (S) g2

)(sinu 22

13. Assertion : For a projectile up the incline maximum angle of projection can be

24 where is angle

made by incline with horizontal.

Reason : Maximum range up the incline is given by )sin1(gu2

where is angle made by incline with

horizontal..(A) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion.(B) If both Assertion and Reason are true, but Reason is not correct explanation of the Assertion.(C) if Assertion is true, but the Reason is false.(D) if Assertion is false, but the Reason is true.

14. STATEMENT-1 : Two stones are simultaneously projected from level ground from same point with samespeeds but different angles with horizontal. Both stones move in same vertical plane. Then the twostones may collide in mid air.STATEMENT-2 : For two stones projected simultaneously from same point with same speed at differentangles with horizontal, their trajectories may intersect at some point.(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1(C) Statement-1 is True, Statement-2 is False(D) Statement-1 is False, Statement-2 is True

Answer Key (Revision Test - 02)1. (D) 2. (C) 3. (A) 4. (A) 5. (A) 6. (B) 7. (D)8. (D) 9. (B) 10. (B) 11. (C) 12. (a) S (b) R (c) Q (d) P13. (D) 14. (D)


RESONANCE 1



Instructions :1. For each correct single choice question 3 marks (with 1 mark negative making).2. For each correct multiple choice question 3 marks (with 1 mark negative making).3. For each correct answer in comprehension 4 marks (with 1 mark negative marking).4. For each correct assertion/reason question 3 marks (with 1 mark negative marking).5. For each correct subjective question 6 marks (with no negative marking).

1. Two blocks A & B with mass 4 kg and 6 kg respectively are connectedby a stretched spring of negligible mass as in figure. When the twoblocks are released simultaneously the initial acceleration of B is1.5 m/s2 westward. The acceleration of A is :(A) 1 m/s2 westward (B) 2.25 m/s2 eastward(C) 1 m/s2 eastward (D) 2.75 m/s2 westward

2. System shown in figure is in equilibrium. The magnitude of change intension in the string just before and just after, when one of the spring iscut. Mass of both the blocks is same and equal to m and springconstant of both springs is k. (Neglect any effect of rotation)

(A) 2

gm(B)

4

gm(C)

4

gm3(D)

2

gm3

3. In the figure a block �A� of mass �m� is attached at one end of a light spring and the

other end of the spring is connected to another block �B� of mass 2m through a light

string. �A� is held and B is in static equilibrium. Now A is released. The acceleration

of A just after that instant is �a�. In the next case, B is held and A is in static

equilibrium. Now when B is released, its acceleration immediately after the releaseis 'b'. The value of a/b is : (Pulley, string and the spring are massless)

(A) 0 (B) undefined (C) 2 (D) 21

4. In the figure, at the free end of the light string, a force F is applied to keep thesuspended mass of 18 kg at rest. Then the force exerted by the ceiling on thesystem (assume that the string segments are vertical and the pulleys are light andsmooth) is: (g= 10 m/s2)

(A) 60 N (B) 120 N (C) 180 N(D) 240 N (E) 200 N

5. Two massless rings slide on a smooth circular loop of the wire whose axis lies ina horizontal plane. A smooth massless inextensible string passes through therings, which carries masses m

1 & m

2 at the two ends and mass m

3 between the

rings. If there is equilibrium when the line connnecting each ring with centresubstends an angle 300 with vertical as shown in figure. Then the ratio of masses are (A) m

1 = 2m

2 = m

3(B) 2m

1 = m

2 = 2m

3(C) m

1 = m

2 = m

3 (D) None of these

6. Four identical metal butterflies are hanging from a light string of length 5 at equallyplaced points as shown. The ends of the string are attached to a horizontal fixedsupport. The middle section of the string is horizontal. The relation between theangle

1 and

2 is given by

1

2

(A) sin1 = 2 sin

2(B) 2cos

1 = sin

2

(C) tan1 = 2 tan

2(D)

2 <

1 and no other conclusion can be derived.

REVISION TEST - 03COURSE : VIJAY (R)

TOPIC : NLM & FrictionSUBJECT : PHYSICS


RESONANCE 2

7. A bob is hanging over a pulley inside a car through a string . Thesecond end of the string is in the hand of a person standing in the car. The car is moving with constant acceleration 'a' directed horizontallyas shown in figure . Other end of the string is pulled with constantacceleration '

a

' (relative to car) vertically. The tension in the string is

equal to

(A) m 22 ag (B) m 22 ag � ma (C) m 22 ag + ma (D) m(g + a)

8. A wedge of height 'h' is released from rest with a light particle P placed on it asshown. The wedge slides down an incline which makes an angle with thehorizontal. All the surfaces are smooth, P will reach the surface of the inclinein time

(A)

2sing

h2(B)

cossingh2

(C) tang

h2(D)

2cosg

h2

9. In the given arrangement, mass of the block is M and the surface onwhich the block is placed is smooth. Assuming all pulleys to bemassless and frictionless, strings to be inelastic and light, R

1, R

2 and

R3 to be light supporting rods, then acceleration of point �P� will be

(Ais fixed) :

(A) 0 (B) (C) mF4

(D) mF2

10. In the arrangement shown in the figure mass of the block B and A are 2 m,, 8 mrespectively. Surface between B and floor is smooth. The block B is connectedto block C by means of a pulley. If the whole system is released then theminimum value of mass of the block C so that the block A remains stationarywith respect to B is :(Co-efficient of friction between A and B is and pulley is ideal)

(A) m

(B)

2

1

m

(C)

10

1

m

(D) 1

m10

11. A plank is held at an angle to the horizontal (Fig.) on two fixed supportsA and B. The plank can slide against the supports (without friction) becauseof its weight Mg. With what acceleration and in what direction, a man ofmass m should move so that the plank does not move.

(A) g sin

M

m1 down the incline (B) g sin

m

M1 down the incline

(C) g sin

Mm

1 up the incline (D) g sin

mM

1 up the incline

12. A block of mass 20 kg is acted upon by a force F = 30 N at an angle 53° with the

horizontal in downward direction as shown. The coefficient of friction between theblock and the horizontal surface is 0.2. The friction force acting on the block by theground is (g = 10 m/s2)

F53°

(A) 40.0 N (B) 30.0 N (C) 18.0 N (D) 44.8 N

13. A particle is resting over a smooth horizontal floor. At t = 0, a horizontal forcestarts acting on it. Magnitude of the force increases with time according to lawF = t, where is a positive constant and t is time. For the figure shown whichof the following statements is/are correct?

(A) Curve 1 shows acceleration against time (B) Curve 2 shows velocity against time(C) Curve 2 shows velocity against acceleration (D) none of these

RESONANCE 3

14. An insect of mass m, starts moving on a rough inclined surface frompoint A. As the surface is very sticky, the coefficient of friction betweenthe insect and the incline is = 1. Assume that it can move in any

direction ; up the incline or down the incline then =37°

=1

A

(A) The maximum possible acceleration of the insect can be 14 m/sec2

(B) The maximum possible acceleration of the insect can be 2 m/sec2

(C) The insect can move with a constant velocity

(D) The insect can not move with a constant velocity

ComprehensionA block of mass M is kept in elevator (lift) which starts moving upward with constant acceleration 'b' as shownin figure. Initially elevator at rest. The block is observed by two observers A and B for a time interval t = 0 tot = T. Observer B is at rest with respect to elevator and observer A is standing on the ground.

15. The observer A finds that the work done by gravity on the block is -

(A) 21

Mg2T2 (B) �21

Mg2T2 (C) 21

Mg bT2 (D) �

21

Mg bT2

16. The observer A finds that work done by normal reaction acting on the block is -

(A) 21

M(g + b)2T2 (B) �21

M(g + b)2T2 (C) 21

M(g + b) bT2 (D) �

21

M(g + b) bT2

17. According to observer B(A) The work done by gravity on the block is zero(B) The work done by normal reaction on the block is zero(C) The work done by pseudo force on the block is zero(D) All the above are correct

Q.18 to 23(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1(C) Statement-1 is True, Statement-2 is False(D) Statement-1 and Statement-2 both are False.(E) Statement-1 is False, Statement-2 is True.

18. Assertion (A) : If a body is not in rest position then the net external force acting on it cannot be zero.Reason (R) : If a body is moving with uniform speed it will continue doing so unless frictional force exceedsthe force of motion.

19. Assertion (A) : Two bodies of mass 50g and 20g are allowed to fall from the same height. If air resistance foreach is same, then both the bodies reach the earth simultaneously.Reason (R) : Acceleration of both the bodies is same.

20. Assertion (A) : Air is thrown on a sail attached to a boat from an electric fan placed on the boat, because ofwhich some movement is caused in the boat.Reason (R) : When the fan pushes the sail by the air, then air also pushes the fan in the opposite direction,causing motion.

21. Assertion (A) : A bird sitting on the floor of a wire cage and cage is in the hand of a boy. Even when the birdstarts flying in the cage, the boy does not experience any change in the weight of the cage.Reason (R) : Bird is still in the cage because of which the boy does not experience any change.

RESONANCE 4

22. Assertion (A) : A soda water bottle is falling freely the bubbles of the gas will not rise in water.Reason (R) : Pressure in the water does not increase with depth.

23. Assertion (A) : When a ball is thrown upwards, its momentum first decreases and then increases.Reason (R) : Law of conservation of momentum is not followed is this process.

24. Figure shows a moving truck, in which there is a bob 'A' and a block 'B'attached to a spring kept on the rough floor of truck. With respect totruck, (g = 10 m/sec2) (Assume spring is massless)

(a) If bob A is in equilibrium at = 30º, the spring is in its natural state and the block B

(mass = 3 kg) is also in equilibrium , find the minimum value of the coefficient of static

friction between the block and the floor of truck.(b) If now the acceleration of truck is changed so that the new angular position of A for which it is

again in equilibrium is 45º, find the minimum elongation in spring when block B is in equilibrium

assuming the value of the coefficient of static friction as that calculated in part (a).

25. Collar A starts from rest & moves to the left with a constant acceleration.Knowing that after 30 s, the relative velocity of collar B w.r.t. collar A is900 mm/s, determine the accelerations of A and B.

26. In the arrangement shown in Figure mass of blocks A, B and C is 18.5 kg, 8 kgand 1.5 kg respectively. All the surfaces are smooth. System is released fromrest at t = 0 & pulleys are light & frictionless. Calculate acceleration of block C.

27. Figure shows an ideal pulley block of mass m = 1 kg, resting on a rough groundwith friction coefficient µ = 1.5. Another block of mass M = 11 kg is hanging asshown. When system is released it is found that the magnitude of acceleration ofpoint P on string is a. Find value of 4a in m/s2. (Use g = 10 m/s2)

28. In which of the following cases the magnitude of acceleration of the block A will be maximum (Neglectionfriction, mass of pulley and string)

(i)

Am 2m

(ii)

Am 2mg

(iii) A

2mg

msmooth

(iv) A

B 2m

m

Answer Key (Revision Test - 03)1. B 2. A 3. C 4. D 5. C 6. C7. C 8. A 9. C 10. D 11. B 12. C13. A,B,C 14. A,C 15. D 16. C 17. D 18. D19. D 20. D 21. D 22. A 23. A

24. (a) 3

1(b) 13 25. 10mm/s2

26. (i) 10 ms2 (ii) 0. 19 joule27. 13

28. (i) a = m3

mgmg2 =

3g

(ii) a = m

mgmg2 = g (iii) a =

mmg2

= 2g (iv) a = 3g2


RESONANCE 1

REVISION TEST - 04SUBJECT : PHYSICSCourse : VIJAY (R)

TOPIC : WPE & Circular Motion


Instructions :1. For each correct single choice question 3 marks (with 1 mark negative marking).2. For each correct multiple choice question 4 marks (with 1 mark negative marking).3. For each correct answer in comprehension 4 marks (with 1 mark negative marking).4. For each correct answer in match the column 6 marks (with no negative marking).4. For each correct assertion/reason question 3 marks (with 1 mark negative marking).5. For each correct subjective question 6 marks (with no negative marking).


1. Select the correct alternative.(A) Work done by kinetic friction on a body always results in a loss of its kinetic energy.(B) Work done on a body, in the motion of that body over a close loop is zero for every force in nature.(C) Total mechanical energy of a system is always conserved no matter what type of internal andexternal forces on the body are present.(D) When total work done by a conservative force on the system is positive then the potential energyassociated with this force decreases.

2. A body of mass 1 kg is shifted from A to D on inclined planes by applying a force slowly such that theblock is always is in contact with the plane surfaces. Neglecting the jerk experienced at points C andB, total work done by the force is :

(A) 90 J (B) 56 J (C) 180 J (D) 0 J

3. The cart starting from rest moves down the incline. When the cart maximally compresses the spring (thatis compression in the spring is maximum) at the bottom of the track, the cart�s(A) velocity and acceleration are zero.(B) velocity is nonzero but its acceleration is zero.(C) acceleration is nonzero, but its velocity is zero.(D) velocity and acceleration are both nonzero.

4. A horse drinks water from a cubical container of side 1 m. The level of the stomachof horse is at 2 m from the ground. Assume that all the water drunk by the horse isat a level of 2 m from the ground. Then minimum work done by the horse in drinkingthe entire water of the container is (Take

water = 1000 kg/m3 and g = 10 m/s2 ) :

(A) 10 kJ (B) 15 kJ (C) 20 kJ (D) zero


RESONANCE 2

5. A man places a chain (of mass �m� and length � �) on a table slowly. Initially the lower end of the chain just

touches the table. The man drops the chain when half of the chain is in vertical position. Then work done bythe man in this process is :

(A) � mg 2

(B) � 4

mg(C) �

8mg3

(D) � 8

mg

6. In the track shown in figure section AB is a quadrant of a circle of 1 metre radius. Ablock is released at A and slides without friction until it reaches B. After B it moveson a rough horizontal floor and comes to rest at distance 3 metres from B. What isthe coefficient of friction between floor and body ?(A) 1/3 (B) 2/3 (C) 1/4 (D) 3/8

7. A particle of mass m moving along a straight line experiences force F whichvaries with the distance travelled as shown in the figure. If the velocity of the

particle at x0 is

2 0 0F x

m, then velocity at 4

x

0 is:

(A) 2 m

xF2 00 (B) 2 mxF 00 (C)

mxF 00 (D) none of these

8. A block of mass m starts at rest at height h on a frictionless inclinedplane. The block slides down the plane, travels across a rough horizontalsurface with coefficient of kinetic friction , and compresses a spring withforce constant k a distance x before momentarily coming to rest. Thenthe spring extends and the block travels back across the rough surface,sliding up the plane. The block travels a total distance d on rough horizontalsurface. The correct expression for the maximum height h� that the block

reaches on its return is:(A) mgh� = mgh � mgd (B) mgh� = mgh + mgd(C) mgh� = mgh + mgd + kx2 (D) mgh� = mgh � mgd � kx2

9. The figure shows a hollow cube of side 'a' of volume V. There is a small chamber of volume 4V

in the cube as

shown. This chamber is completely filled by m kg of water. Water leaks through a hole H and spreads in thewhole cube. Then the work done by gravity in this process assuming that the complete water finally lies atthe bottom of the cube is :

(A) 21

mg a (B) 83

mg a (C) 85

mga (D) 81

mga

10. A particle is moving in a circular path. The acceleration and momentum vectors at an instant of time are

a

= 2 i� + 3 j� m/s2 and P

= 6 i� � 4 j� kgm/s. Then the motion of the particle is(A) uniform circular motion (B) circular motion with tangential acceleration(C) circular motion with tangential retardation (D) we cannot say anything from a

and P

given here.

RESONANCE 3

11. A bead of mass m is located on a parabolic wire with its axis vertical and vertex at the origin as shown infigure and whose equation is x2 = 4ay. The wire frame is fixed and the bead can slide on it without friction. Thebead is released from the point y = 4a on the wire frame from rest. The tangential acceleration of the beadwhen it reaches the position given by y = a is :

(A) 2g

(B) 2g3

(C) 2

g(D)

5

g

12. TTwo particles tied to different strings are whirled in a horizontal circle as shown in figure. The ratio oflengths of the strings so that they complete their circular path with equal time period is:

(A) 23

(B) 32

(C) 1 (D) None of these

13. A smooth and vertical cone-shaped funnel is rotated with an angular velocity in such a way that an object on the inner wall of the funnel is at rest w.r.t. thefunnel. If the object is slightly displaced along the slope from this position andreleased :(A) it will be in equilibrium at its new position.(B) it will execute SHM(C) it will oscillate but the motion is not SHM(D) none of these

14. A ring of radius R lies in vertical plane. A bead of mass �m� can move along the ring

without friction. Initially the bead is at rest at the bottom most point on ring. Theminimum constant horizontal speed v with which the ring must be pulled such thatthe bead completes the vertical circle

(A) gR3 (B) gR4 (C) gR5 (D) gR5.5

15. A simple pendulum is oscillating in a vertical plane. If resultant acceleration of bob of mass m at a point A isin horizontal direction, find the tangential force at this point in terms of tension T and mg.

(A) mg (B) T

mg 22 )mg(T (C) T

mg22 T)mg( (D) mg

T22 T)mg(

16. The member OA rotates about a horizontal axis through O with a constantcounter clockwise velocity = 3 rad/sec. As it passes the position = 0, asmall mass m is placed upon it at a radial distance r = 0.5 m. If the mass isobserved to slip at = 37º, the coefficient of friction between the mass & the

member is ______.

(A) 163

(B) 169

(C) 94

(D) 95

RESONANCE 4

17. A bob is attached to one end of a string other end of which is fixed at peg A.The bob is taken to a position where string makes an angle of 300 with thehorizontal. On the circular path of the bob in vertical plane there is a peg �B� at

a symmetrical position with respect to the position of release as shown in thefigure. If Vc and Va be the minimum speeds in clockwise and anticlockwisedirections respectively, given to the bob in order to hit the peg �B� then ratio

Vc : Va is equal to :

(A) 1 : 1 (B) 1 : 2 (C) 1 : 2 (D) 1 : 4

18. A disc of radius R has a light pole fixed perpendicular to the disc at thecircumference which in turn has a pendulum of length R attached to its otherend as shown in figure. The disc is rotated with a constant angular velocity .The string is making an angle 300 with the rod. Then the angular velocity ofdisc is:

(A)

2/1

Rg3

(B)

2/1

R2g3

(C)

2/1

R3

g

(D)

2/1

R33

g2

19. An automobile enters a turn of radius R. If the road is banked at an angle of 450 and the coefficient offriction is 1, the minimum and maximum speed with which the automobile can negotiate the turnwithout skidding is :

(A) 2rg

and rg (B) 2

rg and rg (C)

2

rg and rg2 (D) 0 and infinite

20. A particle is projected horizontally from the top of a tower with a velocity v0. If v be its velocity at anyinstant, then the radius of curvature of the path of the particle at the point (where the particle is at thatinstant) is directly proportional to :(A) v3 (B) v2 (C) v (D) 1/v


21. A double conical pendulum consists of two masses, m and M, connectedby a massless string passing over a frictionless, massless pulley. Theentire apparatus rotates freely at constant angular speed (rad/s) aboutthe vertical axis (dashed line) passing through centre of pulley as shown.After the system comes in steady state, the length of string on eithersides of pulley are small and L. Pick up the correct option(s).

(A) Mm

coscos

(B) cos =

L

g2

(C) m = ML (D) cos =

2

g

22. One of the forces acting on a particle is conservative then which of the following statement(s) are trueabout this conservative force(A) Its work is zero when the particle moves exactly once around any closed path.(B) Its work equals the change in the kinetic energy of the particle(C) Then that particular force must be constant.(D) Its work depends on the end points of the motion, not on the path between.

23. In the figure, a block rests on the top of a smooth fixedhemispherical tube of radius R in which it can just fit. Twosprings are connected to the base as shown. The block isgiven a small jerk so that it can slide on the hemisphere. TheF-X (F is magnitude of force and x is compression) graph forthe springs is given below. Which of the following may bepossible : (A) The block will compress both springs by same amount.(B) The block will compress the springs during its to and fro motion about its original position by

different amounts.(C) The block will perform to and fro motion along the hemispherical surface about the original position.(D) The block can never come to the original position.

RESONANCE 5

ComprehensionOne end of massless inextensible string of length is fixed and other end is tied to a small ball of mass m.

The ball is performing a circular motion in vertical plane. At the lowest position, speed of ball is g20 .

Neglect any other forces on the ball except tension force and gravitational force. Acceleration due to gravityis g.

24. Motion of ball is in nature of(A) circular motion with constant speed(B) circular motion with variable speed(C) circular motion with constant angular acceleration about centre of the circle.(D) none of these

25. At the highest position of ball, tangential acceleration of ball is -(A) 0 (B) g (C) 5 g (D) 16 g

26. During circular motion, minimum value of tension in the string -(A) zero (B) mg (C) 10 mg (D) 15 mg

Comprehension :A body of mass m is moving along x-axis under the influence of conservative force with a potential energy

given by U(x) = 22 ax

cx

Where c and a are positive constants. When displaced slightly from stable equilibrium position x = x0, it will

experience restoring force proportional to its displacement, the force constant being

0xx2

2

dx

Ud

27. The magnitude of force is maximum at :(A) x = 0 (B) x = + a (C) x = � a (D) no value of x

28. The body is in stable equilibrium at(A) x = 0 (B) x = +a (C) x = � a (D) both x = ± a

29. If body is at x = x0 where (i) x

0 = 2a (ii) x

0 = +a (iii) x

0 = � a.

If it is displaced slightly towards right, it will experience restoring force in(A) all the three cases (B) case (ii) only(C) case (iii) only (D) cases (i) and (ii) only.

30. Match the statements in Column with the results in Column and indicate your answer by darkeningappropriate bubbles in the 4 × 4 matrix given in the OMR.

Column � I Column � II

(a) Work done by ideal gas during free expansion (P) zero(b) A wedge block system is as shown in the fig. (Q) non zero

The wedge lying on horizontal surface is accelerated toright by a horizontal force F. All surfaces are smooth. Workdone by normal reaction exerted by wedge on block in any

time interval is

(c) Two identical conducting spheres of radius 'a' are separated (R) negativeby a distance 'b' (b>>a). Both spheres carry equal andopposite charge. Net electrostatic potential energy ofsystem of both spheres is

(d) A uniform cylinder lies over a rough horizontal platform. The (S) positiveplatform is accelerated horizontally as shown with accelerationa. The cylinder does not slip over the platform.The work doneby the force of friction on the cylinder w.r.t ground in any time interval is

RESONANCE 6

31. A particle is moving with speed v = 2t2 on the circumference of circle of radius R. Match the quantitiesgiven in column-I with corresponding results in column-II

Column-I Column-II

(A) Magnitude of tangential acceleration of particle (p) decreases with time.(B) Magnitude of Centripetal acceleration of particle (q) increases with time(C) Magnitude of angular speed of particle (r) remains constant with respect to centre of circle(D) Angle between the total acceleration vector (s) depends on the value of radius R and centripetal acceleration vector of particle

32. In column-I condition on velocity, force and acceleration of a particle is given. Resultant motion is

described in column-II. u

= initial velocity, F

= resultant force and v

= instantaneous velocity..Column-I Column-II

(A) 0Fu

and F

= constant (p) path will be circular path

(B) 0Fu

and F

= constant (q) speed will increase

(C) 0Fv

all the time and |F

| = constant (r) path will be straight lineand the particle always remains in one plane.

(D) j�3i�2u

and acceleration at all time j�9i�6a

(s) path will be parabolic

33. Each situation in column I gives graph of a particle moving in circular path. The variables , and t representangular speed (at any time t) , angular displacement (in time t) and time respectively. Column gives certainresulting interpretation. Match the graphs in column with statements in column and indicate your answerby darkening appropriate bubbles in the 4 × 4 matrix given in the OMR.

(A) (p) Angular acceleration of particle is uniform

(B)

2

- graph2

(q) Angular acceleration of particle is non-uniform

(C)

- t graph

t

(r) Angular acceleration of particle is directly proportional to t.

(D)

- t graph2

t2(s) Angular acceleration of particle is directly proportional to .

RESONANCE 7

34. Net force on a system of particles in ground frame is zero. In each situation of column-I a statement isgiven regarding this system. Match the statements in column-I with the results in column-II.

Column-I Column-II(A) Acceleration of centre of mass of system (p) is constant

from ground frame(B) Net momentum of system from ground frame. (q) is zero(C) Net momentum of system from frame of centre (r) may be zero

of mass of system(D) K.E. of system from frame of centre of mass (s) may be constantof system

35. STATEMENT-1 : The sum of potential and kinetic energy for a system of moving objects is conserved onlywhen no net external force acts on the objectsSTATEMENT-2 : If no nonconservative force acts on a system of objects, the work done by external forceson a system of objects is equal to change in potential energy plus change in kinetic energy of the system.(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1(C) Statement-1 is True, Statement-2 is False(D) Statement-1 is False, Statement-2 is True

36. STATEMENT-1 : One end of ideal massless spring is connected to fixedvertical wall and other end to a block of mass m initially at rest onsmooth horizontal surface. The spring is initially in natural length. Nowa horizontal force F acts on block as shown. Then the maximumextension in spring is equal to maximum compression in spring.

STATEMENT-2 : To compress and to expand an ideal unstretched spring by equal amount, same workis to be done on spring.

37. STATEMENT-1 : For a particle moving in a circular path, if direction of angular velocity and angularacceleration is same, then angle between its velocity vector and acceleration vector increases.STATEMENT-2 : For a particle moving in a circular path with speed increasing at constant rate, thecentripetal acceleration keeps on increasing(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1(C) Statement-1 is True, Statement-2 is False(D) Statement-1 is False, Statement-2 is True.

38. STATEMENT-1 : A cyclist is cycling on a rough horizontal circular track with increasing speed. Then the netfrictional force on cycle is always directed towards centre of the circular track.STATEMENT-2 : For a particle moving in a circle, component of its acceleration towards centre, that is,centripetal acceleration should exist (except when speed is zero instantaneously).(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1(C) Statement-1 is True, Statement-2 is False(D) Statement-1 is False, Statement-2 is True

SUBJECTIVE QUESTIONS

39. A ring of mass m can slide over a smooth vertical rod. The ring is connected to

a spring of force constant K =4 mg

R where 2

R is the natural length of the

spring. The other end of the spring is fixed to the ground at a horizontal distance2 R from the base of the rod. The mass is released at a height of 1.5 R fromground.(a) calculate the work done by the spring.(b) calculate the velocity of the ring as it reaches the ground.

RESONANCE 8

40. A particle is being acted upon by one dimensional conservative force. In the F�x curve shown, four points A,

B, C, D are marked on the curve. (a) State which type of equilibrium is the particle in at these positions. (b)Is the particle in equilibrium at all these points?

41. A particle of mass 2kg starts to move at position x = 0 and time t = 0 under the action of forceF= (10 + 4x) N along the x-axis on a frictionless horizontal track. Find the power delivered by the forcein watts at the instant the particle has moved by the distance 5m.

42. A rod AB is moving on a fixed circle of radius R with constant velocity �v� as shown in figure. P is the point of

intersection of the rod and the circle. At an instant the rod is at a distance x = 5R3

from centre of the circle.

The velocity of the rod is perpendicular to the rod and the rod is always parallel to the diameter CD.

(a) Find the speed of point of intersection P.(b) Find the angular speed of point of intersection P with respect to centre of the circle.

43. The block of mass m initially at x = 0 is acted upon by a horizontal force F = a bx2(where a > mg), as

shown in the figure. The co-efficient of friction between the surfaces of contact is . The net work done on theblock is zero, if the block travels a distance of ______.

Answer Key (Revision Test - 04)1. D 2. A 3. C 4. B 5. C 6. A 7. D8. A 9. C 10. D 11. C 12. B 13. D 14. B15. B 16. A 17. C 18. D 19. D 20. A 21.A,B,C,D22. A,D 23. B,C 24. B 25. A 26. D 27. A 28. B29. D30. (A) p (B) q,s (C) q,s (D) q,s 31. (A) q (B) q, s (C) q, s (D) p, s32. (A) r (B) q,s (C) p (D) q,r 33. (A) q,s (B) p (C) p (D) q,r34. (A) p,q (B) p,r (C) p,q (D) r,s 35. D 36. D 37. D 38. D

39.mg R

2, 2 gR

40. (a) Point A No equilibriumB Unstable equilibriumC Stable equilibriumD Neutral equilibrium

(b) No, point A, F 0 i.e. particle is not in equilibrium

41. 300 42. (a)VP =

45

V (b) = RVP =

R4V5

43. x = [3(a � mg)/b]½


RESONANCE 1


TOPIC : CENTER OF MASS Time : 3 Hrs. Max. Marks : 129

Instructions :1. For each correct single choice question 3 marks (with 1 mark negative marking).2. For each correct answer in comprehension 4 marks (with 1 mark negative marking).3. For each correct answer in match the column 6 marks (with no negative marking).4. For each correct assertion/reason question 3 marks (with 1 mark negative marking).5. For each correct subjective question 6 marks (with no negative marking).


1. From the circular disc of radius 4 R two small disc of radius R are cut off. Thecentre of mass of the new structure will be : (Centre of lower circular cavity lieson x-axis and centre of upper circular cavity lies on y-axis)

(A) 5R

j�5R

i� (B) 5R

j�5R

i� (C) 5R

j�5R

i� (D) )j�i�(14R3

2. The centre of mass of a non uniform rod of length L whose mass per unit length varies as

= Lx.k 2

where k is a constant & x is the distance of any point on rod from its one end, is (from the same end)

(A) 43

L (B)41

L (C) Lk

(D) Lk3

3. Two semicircular rings of linear mass densities and 2 and of radius �R� each are joined to form a

complete ring. The distance of the center of the mass of complete ring from its centre is :

(A) 8R3

(B) 3R2

(C) 4R3

(D) none of these

4. Both the blocks shown in the given arrangement are given together ahorizontal velocity towards right. If a

cm be the subsequent acceleration of

the centre of mass of the system of blocks, then acm

equals (before slidingstops at all surfaces)(A) 0 m/s2 (B) 5/3 m/s2 (C) 7/3 m/s2 (D) 2 m/s2

5. Two men �A� and �B� are standing on a plank. �B� is at the middle of the

plank and �A� is the left end of the plank. System is initially at rest and

masses are as shown in figure. �A� and �B� starts moving such that the

position of �B� remains fixed with respect to ground then�A� meets �B�.

Then the point where A meets B is located at :

(A) the middle of the plank (B) 30 cm from the left end of the plank(C) the right end of the plank (D) None of these

6. Two balls of same mass are released simultaneously from heights h & 2h from the ground level. The ballscollides with the floor & sticks to it. Then the velocity-time graph of centre of mass of the two balls is bestrepresented by :

(A) (B) (C) (D)

7. A cannon shell moving along a straight line bursts into two parts. Just after the burst one part moves withmomentum 40 Ns making an angle 30º with the original line of motion. The minimum momentum of the

other part of shell just after the burst is :(A) 0 Ns (B) 10 Ns (C) 20 Ns (D) 17.32 Ns

8. Particle 'A' moves with speed 10 m/s in a frictionless circular fixed horizontal pipeof radius 5 m and strikes with 'B' of double mass that of A. Coefficient of restitutionis 1/2 and particle 'A' starts its journey at t = 0. The time at which second collisionoccurs is :

(A) 2

s (B) 32

s (C) 2

5s (D) 4 s


RESONANCE 2

9. Three identical balls of mass m and radius R are placed on frictionless horizontal x-y plane. Ball A at (0, 0),

Ball B at (4R, � 2 R) and ball C at (8R, � 2 2 R). Ball A is suddenly given an impulse i�mV2P

. Ifcollision between balls A and B is perfectly elastic while between B and C is perfectly inelastic, then therelative velocity of ball A with respect to ball C after a long time will be:

(A) j�22

Vi�

22

V (B) j�

22

Vi�

22

V (C) j�

22

V3i�

22

V (D) j�

22

V3i�

22

V

10. A particle of mass m is moving along the x-axis with speed v when itcollides with a particle of mass 2m initially at rest. After the collision, thefirst particle has come to rest, and the second particle has split into twoequal-mass pieces that are shown in the figure. Which of the followingstatements correctly describes the speeds of the two pieces ? ( > 0)(A) Each piece moves with speed v.(B) Each piece moves with speed v/2.(C) One of the pieces moves with speed v/2, the other moves with speed greater than v/2(D) Each piece moves with speed greater than v/2.

11. A trolley filled with sand is moving with a velocity v on a smooth horizontal surface due to inertia. If the sandfalls off at the rate of kg/sec, the velocity of the trolley as a function of time will be best represented by :

(A) (B) (C) (D)

12. In the fig. shown a cart moves on a smooth horizontal surface due to an externalconstant force of magnitude F. The initial mass of the cart is M

0 and velocity is

zero. Sand falls on to the cart with negligible velocity at constant rate kg/s andsticks to the cart. The velocity of the cart at time t is :

(A) F t

M t0 (B)

F t

M0

e t (C) F t

M0

(D) F t

M t0 e t

13. In the figure, the block B of mass m starts from rest at the top of a wedge W ofmass M. All surfaces are without friction. W can slide on the ground. B slidesdown onto the ground, moves along it with a speed v, has an elastic collision withthe wall, and climbs back onto W. (A) B will reach the top of W again.(B) From the beginning, till the collision with the wall, the centre of mass of �B plus W � is stationary.

(C) After the collision, centre of mass of �B plus W� moves with the horizontal component of velocity 2mv

m M

(D) When B reaches its highest position on W, the speed of W is2mv

m M.

ComprehensionFigure shows block A of mass 0.2 kg sliding to the right over a frictionless elevated surface at a speed of 10m/s. The block undergoes a collision with stationary block B, which is connected to a nondeformed springof spring constant 1000 Nm�1. The coefficient ofrestitution between the blocks is 0.5. After thecollision, block B oscillates in SHM with a periodof 0.2 s, and block A slides off the left end of theelevated surface, landing a distance 'd' from thebase of that surface after falling height 5m. (use2 = 10; g = 10 m/s2) Assume that the springdoes not affect the collision.

14. Mass of the block B is(A) 0.4 kg (B) 0.8 kg (C) 1 kg (D) 1.2 kg

15. Amplitude of the SHM as being executed by block B-spring system, is

(A) 2.5 10 cm (B) 10 cm (C) 3 10 cm (D) 5 10 cm

16. The distance 'd' will be equal to(A) 2m (B) 2.5 m (C) 4m (D) 6.25 m

RESONANCE 3

ComprehensionFigure shows an irregular wedge of mass m placed on a smooth horizontal surface. Part BC is rough.Theother part of the wedge is smooth.

17. What minimum velocity should be imparted to a small block of samemass m so that it may reach point B:

(A) gH2 (B) gH2 (C) )hH(g2 (D) gh

18. The velocity of wedge when the block comes to rest (w.r.t. wedge) on part BC is :

(A) gH (B) hH(g (C) gH2 (D) none of these

19. If the coefficient of friction between the block and wedge is , and the block comes to rest with respect towedge at a point D on the rough surface then BD will be

(A)

H(B)

hH(C)

h(D) none of these

Comprehension :A smooth rope of mass m and length L lies in a heap on a smooth horizontal floor, with one end attached to a block of mass M. The block is given asudden kick and instantaneously acquires a horizontal velocity ofmagnitude V

0 as shown in figure 1. As the block moves to right pulling the

rope from heap, the rope being smooth, the heap remains at rest. At theinstant block is at a distance x from point P as shown in figure-2 (P is apoint on the rope which has just started to move at the given instant) ,choose correct options for next three question.

20. The speed of block of mass M is

(A) )xLm

M(

mV0

(B)

)xLm

M(

MV0

(C)

)xLm

M(M

Vm 02

(D)

)xLm

M(m

VM 02

21. The magnitude of acceleration of block of mass M is

(A) 3

20

3

)xLm

M(

V

Lm

(B)

3

20

2

)xLm

M(

V

LmM

(C)

3

20

4

)xLm

M(

V

LMm

(D)

3

20

2

)xLm

M(

V

LM

22. The tension in rope at point P is

(A) 2

20

2

)xLm

M(

V

LmM

(B)

2

20

2

)xLm

M(

V

LMm

(C)

2

20

3

)xLm

M(

V

Lm

(D) 2

20

3

)xLm

M(

V

LM

23. In each situation of column-I a mass distribution is given and information regarding x and y-coordinate ofcentre of mass is given in column-II. Match the figures in column-I with corresponding information of centreof mass in column-II.

Column-I Column-II(A) An equilateral triangular wire (p) x

cm > 0

frame is made using three thinuniform rods of mass per unit lengths , 2 and 3 as shown

(B) A square frame is made using (q) ycm

> 0four thin uniform rods of massper unit length lengths , 2, 3 and 4 as shown

(C) A circular wire frame is made (r) xcm

< 0of two uniform semicircular wiresof same radius and of mass per unit length and 2 as shown

(D) A circular wire frame is made (s) ycm

< 0of four uniform quarter circularwires of same radius and mass per unit length , 2, 3and 4 as shown

RESONANCE 4

24. Two identical uniform solid spheres of mass m each approach each other with constant velocities such thatnet momentum of system of both spheres is zero. The speed of each sphere before collision is u. Both thespheres then collide. The condition of collision is given for each situation of column-I. In each situation ofcolumn- information regarding speed of sphere(s) is given after the collision is over. Match the condition ofcollision in column- with statements in column-.

Column- Column-(A) Collision is perfectly elastic and head on (p) speed of both spheres after collision is u(B) Collision is perfectly elastic and oblique (q) velocity of both spheres after

collision is different

(C) Coefficient of restitution is e = 21

and (r) speed of both spheres after collision

collision is head on is same but less than u.

(D) Coefficient of restitution is e = 21

and (s) speed of one sphere may be more than u.

collision is oblique25. STATEMENT-1 : Two spheres undergo a perfectly elastic collision. The kinetic energy of system of both

spheres is always constant. [There is no external force on system of both spheres].STATEMENT-2 : If net external force on a system is zero, the velocity of centre of mass remains constant.(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1(C) Statement-1 is True, Statement-2 is False(D) Statement-1 is False, Statement-2 is True

26. STATEMENT-1 : Non zero work has to be done on a moving particle to change its momentum.STATEMENT-2 : To change momentum of a particle a non zero net force should act on it.(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1(C) Statement-1 is True, Statement-2 is False(D) Statement-1 is False, Statement-2 is True

27. STATEMENT-1 : When a body collides elastically and head on with another identical stationary body on africtionless surface, it losses all of its kinetic energy (No external forces on the system of the two bodies andno rotation of the bodies).STATEMENT-2 : In elastic collisions, only momentum is conserved.(a) If both assertion and reason are true and reason is the correct explanation of assertion(b) If both assertion and reason are true but reason is not the correct explanation of assertion.(c) If assertion is true but reason is false(d) If assertion is false but reason is true(A) a (B) b (C) c (D) d

28. From a uniform square plate the shaded portions are removed as shown in figure.Find the coordinates of centre of mass of the remaining plate. X, Y axes and originare shown in figure .

29. In the figure shown two nonconducting blocks of A and B of mass �m�, 2m and

charges � Q, 2Q respectively are attached at the two ends of a light spring of

spring constant �k�. They are kept on a smooth horizontal surface. A and B are

initially at rest and the spring is unstretched. Now a uniform electric field of intensity�E� is switched on pointing towards right. Neglecting the electrostatic interaction

between A and B find the maximum extension of the spring during the motion ofthe system. Also find the acceleration of �B� at the moment of maximum extension

in the spring 30. A coordinate axis system taking x-axis as horizontal smooth floor is shown in

figure. Two small balls of masses m and 3m attached with a string are releasedfrom some heights on y-axis as shown in figure. The balls may collide head on orobliquely. After a certain time mass m is at (9 cm, 20 cm) while mass 3m is 25 cmabove the x axis and the strings is taut. The balls always remain in x-y plane. Findthe length of string.

31. A particle moving on a smooth horizontal surface strikes a stationary wall.The angle of strike is equal to the angle of rebound & is equal to 37° and

the coefficient of restitution with wall is e = 51

. Find the friction coefficient

between wall and the particle in the form 10X

and fill value of X.: //////

//////

//////

//////

//////

//////

37º

37º

Answer Key (Revision Test - 05)1.D 2. A 3. B 4. D 5. C 6. B 7. C 8. C 9. D 10. D 11. D 12. A 13. C,D14. C 15. A 16. B 17. A 18. A 19. B 20. B 21. B 22. A 23. (A) q,r (B) p,s (C) p,s (D) p,s

24. (A) p,q (B) p,q (C) q,r (D) q,r 25. D 26. D 27. C 28.

104a49

,104

a55 29. k3

QE8 30. 13 cm. 31. 5


RESONANCE 1

REVISION TEST - 06SUBJECT : PHYSICSCOURSE : VIJAY (R)

TOPIC : ROTATIONAL MOTION


Instructions :1. For each correct single choice question 3 marks (with 1 mark negative marking).2. For each correct multipal choice question 3 marks (with 1 mark negative marking).3. For each correct answer in comprehension 4 marks (with 1 mark negative marking).4. For each correct assertion/reason question 3 marks (with 1 mark negative marking).5. For each correct subjective question 6 marks (with no negative marking).


1. The moment of inertia of a thin sheet of mass M of the given shape about the specified axis is :

(A) 12

7 Ma2 (B)

12

5 Ma2 (C)

3

1 Ma2 (D)

12

1 Ma2

2. A disc is hinged in a vertical plane about a point on its radius. What will be the distance of the hinge from thedisc centre so that the period of its small oscillations under gravity is minimum?

(A) R (B) 2

R(C)

2R

(D) 4R

3. A uniform ladder of length 5 m and mass 100 kg is in equilibrium between vertical smooth wall andrough horizontal surface. Find minimum friction co-efficient between floor and ladder for this equilibrium.

(A) 1/2 (B) 3/4 (C) 1/3 (D) 2/3

4. Figure shows an arrangement of masses hanging from a ceiling. In equilibrium, each rod is horizontal, hasnegligible mass and extends three times as far to the right of the wire supporting it as to the left. If mass m

4

is 48 kg then mass m1 is equal to :

m4

m3

m2 m1

(A) 1 kg (B) 2 kg (C) 3 kg (D) 4 kg


RESONANCE 2

5. A massless stick of length L is hinged at one end and a mass mattached to its other end. The stick is free to rotate in vertical planeabout an fixed horizontal axis passing through frictionless hinge.The stick is held in a horizontal position. At what distance x fromthe hinge should a second mass M = m be attached to the stick,so that stick falls as fast as possible when released from rest.

(A) L2 (B) L3 (C) L)12( (D) L)13(

6. Two identical discs of mass m and radius r are arranged as shown in the figure. If is the angularacceleration of the lower disc and a

cm is acceleration of centre of mass of the lower disc, then relation

between acm,

& r is :

(A) acm

=

r(B) a

cm = 2 r (C) a

cm =

r (D) none of these

7. A uniform rod of length l rotating with an angular velocity , while its centre

moves with linear velocity v =

6. If the end A of the rod is suddenly fixed, the

angular velocity of the rod will be :

(A)3

4 (B)

3(C)

2(D)

2

3

8. A uniform disc of mass M and radius R is released from the shown position. PQ is a string, OP is ahorizontal line, O is the centre of the disc and distance OP is R/2. Then tension in the string just after thedisc is released will be :

(A) 2

Mg (B)

3Mg

(C) 3Mg2

(D) none of these

9. Mass m is connected with an ideal spring of natural length whose other end is fixed on a smooth horizontaltable. Initially spring is in its natural length . Mass m is given a velocity �v� perpendicular to the spring andreleased. The velocity perpendicular to the spring when its length is + x, will be

(A) x

v2

(B) x

v2 2

(C) x

v

(D) zero

RESONANCE 3

10. A uniform cubical solid block of side a moving with velocity v on a horizontal smooth plane as shown.It hits a fixed ridge at point O. The angular speed of the block just after it hits 'O' is

(A)a3v

(B) a2v

(C) a2v3

(D)a4v3

11. A uniform circular disc placed on a horizontal rough surface has initiallya velocity v

0 and an angular velocity

0 as shown in the figure. The disc comes

to rest after moving some distance in the direction of motion. Then v0/

0 is :

(A) r/2 (B) r (C) 3 r/2 (D) 2

12. Determine the acceleration a of the supporting surface required to keep the centre G of the circularpipe in a fixed position during the motion. No slipping takes place between pipe and its support.

(A) g sin (B) 2g sin (C) g

2sin (D) 2 g sin

13. A solid sphere of mass m and radius r is gently placed on a conveyer belt moving with constant velocity

V. If the coefficient of friction between the belt and sphere is 72

, the distance travelled by the centre of

the sphere before it starts pure rolling is

(A) g7V2

(B) g49V2 2

(C) g5V2 2

(D) g7

V2 2

14. A solid homogeneous cylinder of height h and base radius r is kept vertically on a conveyer belt movinghorizontally with an increasing velocity v = a + bt2. If the cylinder is not allowed to slip then the timewhen the cylinder is about to topple, will be equal to

(A) bhrg

(B) bhrg2

(C) rhbg2

(D) bh2rg

15. A ring of mass m and radius R rolls on a horizontal rough surface without slipping due to an appliedforce �F�. The friction force acting on ring is :

(A) 3F

(B) 3F2

(C) 4F

(D) Zero

RESONANCE 4

16. A uniform disc of mass 2kg and radius 1m is mounted on an axle supported on fixed frictionless bearings. Alight cord is wrapped around the rim of the disc and mass of 1kg is tied to the free end. If it is released fromrest,(A) the tension in the cord is 5N(B) in first 4 seconds the angular displacement of the disc is 40 rad.(C) the work done by the torque on the disc in first 4 sec. is 200J(D) the increase in the kinetic energy of the disc in the first 4 seconds is 200J.

17. Which of the following statements is/are true(A) work done by kinetic friction on an object may be positive.(B) A rigid body rolls up an inclined plane without sliding. The friction force on it will be upwards. (only contact force and gravitational force is acting)(C) A rigid body rolls down an inclined plane without sliding. The friction force on it will be upwards. (only contact force and gravitational force is acting)(D) A rigid body is left from rest from the top of a rough inclined plane. It moves down the plane with slipping.The friction force on it will be upwards.

Comprehension # 1A bicycle has pedal rods of length 16 cm connected to a sprocketed disc of radius 10 cm. The bicyclewheels are 70 cm in diameter and the chain runs over a gear of radius 4 cm. The speed of the cycle isconstant and the cyclist applies 100 N force that is always perpendicular to the pedal rod, as shown.Assume tension in the lower part of chain negligible. The cyclist is peddling at a constant rate of tworevolutions per second. Assume that the force applied by other foot is zero when one foot is exerting100 N force. Negelect friction within cycle parts & the rolling friction.

Chainupper part F=100N

16cm

Sprocket DiscWheel

r=4cm

R=35cm

Gear

18. The tension in the upper portion of the chain is equal to(A) 100 N (B) 120 N (C) 160 N (D) 240 N

19. Net torque on the rear wheel of the bicycle is equal to(A) zero (B) 16 N-m (C) 6.4 N-m (D) 4.8 N-m

20. The power delivered by the cyclist is equal to(A) 280 W (B) 100 W (C) 64 W (D) 32 W

21. The speed of the bicycle is :(A) 6.4 m/s (B) 3.5 m/s (C) 2.8 m/s (D) 5.6 m/s

22. The net force of the friction on the rear wheel due to the road is :(A) 100 N (B) 62 N (C) 32.6 N (D) 18.3 N

Comprehension # 2A square frame of mass m is made of four identical uniform rods of length L each. This frame is placedon an inclined plane such that one of its diagonals is parallel to the inclined plane as shown in figure,and is released.

RESONANCE 5

23. The moment of inertia of square frame about the axis of the frame is :

(A)3

mL2

(B)3

mL2 2

(C)3

mL4 2

(D)12

mL2

24. The frictional force acting on the frame just after the release of the frame assuming that it does notslide is :

(A)3

sinmg (B)

7

sinmg2 (C)

5

sinmg3 (D)

5

sinmg2

25. The acceleration of the center of square frame just after the release of the frame assuming that it doesnot slide is :

(A)3

sing (B)

7

sing2 (C)

5

sing3 (D)

5

sing2

Comprehension # 3A horizontal uniform rod of mass 'm' has its left end hinged to the fixed incline plane, while its right end rests onthe top of a uniform cylinder of mass 'm' which in turn is at rest on the fixed inclined plane as shown. Thecoefficient of friction between the cylinder and rod, and between the cylinder and inclined plane, is sufficient tokeep the cylinder at rest.

26. The magnitude of normal reaction exerted by the rod on the cylinder is

(A) 4

mg(B)

3mg

(C) 2

mg(D)

3mg2

27. The ratio of magnitude of frictional force on the cylinder due to the rod and the magnitude of frictional force onthe cylinder due to the inclined plane is:

(A) 1 : 1 (B) 3:2 (C) 2 : 1 (D) 1:2

28. The magnitude of normal reaction exerted by the inclined plane on the cylinder is:

(A) mg (B) 2mg3

(C) 2mg (D) 4mg5

29. STATEMENT-1 : A disc rolls without slipping on a fixed rough horizontal surface. Then there is no pointon the disc whose velocity is in vertical direction.STATEMENT-2 : Rolling motion can be taken as combination of translation and rotation. Due to thetranslational part of motion a velocity (translational component) exist in horizontal direction for anypoint on the disc rolling on a fixed rough horizontal surface.(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1(C) Statement-1 is True, Statement-2 is False(D) Statement-1 is False, Statement-2 is True.

30. STATEMENT-1 : A rigid disc rolls without slipping on a fixed rough horizontal surface with uniformangular velocity. Then the acceleration of lowest point on the disc is zero.STATEMENT-2 : For a rigid disc rolling without slipping on a fixed rough horizontal surface, the velocityof the lowest point on the disc is always zero.(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1(C) Statement-1 is True, Statement-2 is False(D) Statement-1 is False, Statement-2 is True.

RESONANCE 6

31. STATEMENT-1 : A uniform cubical block(of side a) undergoes translational motion on a smooth horizontalsurface under action of horizontal force F as shown. Under the given condition, the horizontal surfaceexerts normal reaction non-uniformly on lower surface of the block.

STATEMENT-2 : For the cubical block given in statement-1, the horizontal force F has tendency torotate the cube about its centre in clockwise sense. Hence, the lower right edge of cube presses thehorizontal surface harder in comparision to the force exerted by lower left edge of cube on horizontalsurface.(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1(C) Statement-1 is True, Statement-2 is False(D) Statement-1 is False, Statement-2 is True.

32. STATEMENT-1 : A homogeneous rectangular brick lies at rest on a fixed rough inclined plane as shown.Then the right half of the brick exerts greater force on the inclined plane as compared to left half of the brick.

STATEMENT-2 : For brick in situation of statement-1 to be at rest, the net moment of all forces about itscentre of mass should be zero. Moment of force on brick due to its weight about centre of mass is zero. Themoment of force due to friction on brick about its centre of mass has tendency to rotate the brick in clockwisesense. Hence the right half of the brick presses the inclined plane more in comparision to the left half of thebrick.(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1(C) Statement-1 is True, Statement-2 is False(D) Statement-1 is False, Statement-2 is True

33. STATEMENT-1 : A body is purely rolling (rolling without slipping). The velocity of point of contact (ofbody) must be zero with respect to ground.STATEMENT-2 : By definition, pure rolling of a body occurs when velocity of its point of contact is zerorelative to the surface on which it rolls.(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1(C) Statement-1 is True, Statement-2 is False(D) Statement-1 is False, Statement-2 is True

34. Find out the moment of inertia of the following structure (written as ) about axis AB made of

thin uniform rods of mass per unit length .

RESONANCE 7

35. A circular hole of radius R/2 is cut from a thin uniform circular plate of radius R as shown (O is thecentre of the circular plate). If the mass of the remaining plate is M, then find the moment of inertia ofthe plate about an axis through O perpendicular to plane of the plate ?

36. In figure the uniform gate weighs 300 N and is 3 m wide & 2 m high. It issupported by a hinge at the bottom left corner and a horizontal cable at the topleft corner, as shown. Find :

(a) the tension in the cable and

(b) the force that the hinge exerts on the gate (magnitude & direction).

37. The arrangement shown in figure consists of two identical uniform solid cylinders, each of mass m, on whichtwo light threads are wound symmetrically. Find the tension of each thread in the process of motion. Thefriction in the axle of the upper cylinder is assumed to be absent.

38. Two steel ball of equal diameter are connected by a rigid bar of negligible weight as shown and aredropped in the horizontal position from height h above the heavy steel and brass base plates. If thecoefficient of restitution between the ball and steel base is 0.6 and that between the other ball and thebrass base is 0.4. The angular velocity of the bar immediately after rebound is _______. Assume thetwo impacts are simultaneous. (g = 10 m/s2)

39. A ball of diameter d rolls without slipping along a horizontal smooth table top with constant speed v.The ball rolls off the edge falling to the floor a vertical distance h below. While in air the ball makes_______ revolutions.

40. In the figure A & B are two blocks of mass 4 kg & 2 kg respectively attached to the two ends of a light stringpassing over a disc C of mass 40 kg and radius 0.1 m. The disc is free to rotate about a fixed horizontal axes,coinciding with its own axis. The system is released from rest and the string does not slip over the disc. Find:

(i) the linear acceleration of mass B.(ii) the number of revolutions made by the disc at the end of 10 sec. from the start.(iii) the tension in the string segment supporting the block A. (g = 10 m/s2)

RESONANCE 8

41. A rigid cube ABCDEFGH is in motion. At a certain moment, face ABCD is vertical, and the velocities ofvertices A and D are directed vertically downward and equal to v. At the same moment, the speed of pointH equals 2v. What point of the cube has the maximum speed at that moment ? What is that speed ?

42. A uniform ball of radius R rolls without slipping between two rails such that the horizontal distance is dbetween two contact points of the rail to the ball. If R=10cm, d=16cm and the angular velocity is 5rad/svelocity of centre of mass of the ball equals_____ [Pure rolling]

43. A disk of mass M and radius R has a spring of constant k attached to its centre, the other end of thespring being fixed to a vertical wall. If the disk rolls without slipping on a level floor, how far to the rightdoes the centre of mass move, if initially the spring was unstretched and the angular speed of the diskwas

o.

ANSWER KEY1. A 2. B 3. D 4. A 5. C 6. B 7. C8. C 9. C 10. D 11. A 12. A 13. A 14. A15. D 16. A,B,C,D 17. A,B,C,D 18. C 19. A 20. C21. B 22. D 23. A 24. D 25. C 26. C 27. A28. B 29. B 30. D 31. C 32. A 33. D34. 13 3 35. 13/24 MR2 36. (a) T = 225N, (b) FX = 225N, FY = 300N

37. T = 1/10 mg 38. 0.28 rad/sec 39.v

d

h

g

2

40. (i) 10/13 m/s2 (ii) 5000/26 p (iii) 480/13 N 41. vmax

= 22 LL2 = L5

42. 0.3 m/sec 43. Ro3m/2k)

RESONANCE 1


TOPIC : ELECTROSTATICS


Instructions :1. For each correct Single choice question 3 marks (with 1 mark negative marking).2. For each correct Multiple choice question 4 marks (with 1 mark negative marking).3. For each correct answer in Comprehension 4 marks (with 1 mark negative marking).4. For each correct Assertion/Reason question 3 marks (with 1 mark negative marking).5. For each correct Subjective question 6 marks (with no negative marking).6. For each correct Match the column question 6 marks (with no negative marking).


1. Five styrofoam balls are suspended from insulating threads. Several experiments are performed on theballs and the following observations are made :(i) Ball A repels C and attracts B.(ii) Ball D attracts B and has no effect on E.(iii) A negatively charged rod attracts both A and E.An electrically neutral styrofoam ball gets attracted if placed nearby a chargedbody due to induced charge. What are the charges, if any, on each ball ?

A B C

D E

A B C D E(A) + � + 0 +(B) + � + + 0(C) + � + 0 0(D) � + � 0 0

2. Two identical spheres of same mass and specific gravity (which is the ratio of density of a substance anddensity of water) 2.4 have different charges of Q and � 3Q. They are suspended from two strings of same

length fixed to points at the same horizontal level, but distant from each other. When the entire set up istransferred inside a liquid of specific gravity 0.8, it is observed that the inclination of each string in equilibriumremains unchanged. Then the dielectric constant of the liquid is(A) 2 (B) 3 (C) 1.5 (D) None of these

3. A large sheet carries uniform surface charge density . A rod of length 2 has a

linear charge density on one half and - on the second half. The rod is hinged at

mid-point O and makes angle with the normal to the sheet. The electric force

experienced by the rod is &

(A) 0 (B)

sin

2 0

2

(C)

sin

0

2

(D) None of these

4. AB and CD are uniform line charges of infinite length having charge density 1 and

2 and lying along the z

axis and y�axis respectively. The force between them depends on the perpendicular distance between

them, 'r' as, n0

21

r2

.F

, then the value of n is :

(A) 0 (B) 1/2 (C) 1 (D) 2


RESONANCE 2

5. A point charge � q is revolving in a circle of radius ' r

' around a fixed infinite line charge with positive charge

per unit length. Now the point charge is shifted and it revolves in a circle of radius ' 2

r

'. Then:

(A) work done by all forces is zero (B) work done by electrical force is zero(C) work done by external force is zero (D) work done by all forces cannot be zero

6. A ring carries a uniform linear charge density on one half and the linear charge density of same magnitudebut opposite sign on the other half.(A) the component of electric field along the axis at all points on the axis is zero(B) the electric field along the axis and on the axis is zero only at the centre(C) the resultant field at the centre is zero(D) the resultant field at all points on the axis is zero.

7. Two concentric rings, one of radius R and total charge +Q and the second of radius

2R and total charge 8 Q, lie in x-y plane (i.e., z = 0 plane). The common centre

of rings lies at origin and the common axis coincides with z-axis. The charge isuniformly distributed on both rings. At what distance from origin is the net electric

field on z-axis zero. &

(A) 2R

(B) 2

R(C)

22

R(D) R2

8. If the electric potential of the inner shell is 10 volt & that of the outer shell is 5 volt, then the potentialat the centre will be: (the shells are uniformly charged)

(A) 10 volt (B) 5 volt (C) 15 volt (D) 0

9. Find out work done by electric field in shifting a point charge 27

24C from point P to S which are shown in

the figure :

(A) 3

100J (B)

3200

J (C) 100 J (D) 200 J

10. Figure shows three circular arcs, each of radius R and total charge as indicated. The net elecric potential atthe centre of curvature is :

�

R+3Q

30°

45°

+Q

�2Q

(A) R2Q

0(B) R4

Q

0(C) R

Q2

0(D) R

Q

0

RESONANCE 3

11. Figure shows a solid hemisphere with a charge of 5 nC distributed uniformly through its volume. The

hemisphere lies on a plane and point P is located on the plane, along a radial line from the centre ofcurvature at distance 15 cm. The electric potential at point P due to the hemisphere, is :

P

15cm

(A) 150 V (B) 300 V (C) 450 V (D) 600 V

12. A charged particle of charge �Q� is held fixed and another charged particle of mass �m� and charge �q� (of

the same sign) is released from a distance �r�. The impulse of the force exerted by the external agent onthe fixed charge by the time distance between �Q� and �q� becomes 2r is

(A) mr4/Qq 0 (B) r4/Qqm 0

(C) 0 (D) cannot determine

13. A point mass ' m ' and charge ' q ' is projected with a velocity v towards a stationary charge Q0 from adistance of 2 m. The closest distance that q can approach is: [ k = 1/4 0 ]

(A) qQk

Qqkvm

0

02

(B) 0

20

Qqkvm

Qk

(C)

0

20

Qqk

vmQk (D)

0

20

Qqk

vmQk

14. Two smooth spherical non conducting shells each of radius R having uniformly distributed charge Q & Q on their surfaces are released on a smooth non-conducting surface when the distance betweentheir centres is 5 R. The mass of A is m and that of B is 2 m. The speed of A just before A and B collide

is: [Neglect gravitational interaction] (take K = 04

1

)

(A) Rm5Qk2 2

(B) Rm5Qk4 2

(C) Rm5Qk8 2

(D) Rm5Qk16 2

15. Four charges are rigidly fixed along the Y axis as shown. A positive charge approaches the systemalong the X axis with initial speed just enough to cross the origin. Then its total energy at the origin is

(A) zero (B) positive (C) negative (D) data insufficient

16. Two short dipoles k�p & 2p

k� are located at (0, 0, 0) & (1 m, 0, 2 m) respectively. The resultant electric

field due to the two dipoles at the point (1 m, 0, 0) is :

(A)9

32 0

p

k� (B)

7

32 0

p

k� (C)

7

32 0

p

k� (D) none of these

RESONANCE 4

17. Total electric force on an electric dipole placed in an electric field of a point charge is:(A) always zero(B) never zero(C) zero when mid point of dipole coincides with the point charge(D) zero when dipole axis is along any electric line of force.

18. A dipole of dipole moment p is kept at the centre of a ring of radius R and charge Q. The dipole momenthas direction along the axis of the ring. The resultant force on the ring due to the dipole is:

(A) zero (B) 3R

QPk(C) 3R

QPk2

(D) 3R

QPk only if the charge is uniformly distributed on the ring

19. For a system of two dipoles 1P

and 2P

as shown in the figure (both are at origin

and perpendicular to each other along x and y axes respectively)(A) Work done in taking electron from P to R on QPR = 0

(B) tan = )2P1P(2

)2P1P(

(C) tan = )PP(2)PP(

21

21

(D)

r

E

.d r

= 20

21

r24

PP

(P1 and P

2 denotes magnitudes of 1P

and 2P

and r is quite large in comparison to dimensions of

dipoles, E

is resultant electric field and QPR is a quarter of circle whose centre is at O)

20. Two infinitely large charged planes having uniform surface charge density + and � are placed along x-yplane and yz plane respectively as shown in the figure. Then the nature of electric lines of forces in x-z planeis given by :

z

x

�

+

(A)

z

x (B)

z

x (C)

z

x (D)

z

x

21. Two equipotential spherical surfaces having potential 20 V and 0 V are as shown in figure. There is nocharge anywhere in space except on the surface of both the spheres. Then which of the following figurerepresents the nature of electric field in region between the spherical surfaces by electric lines of forces.

20V

0V

(A) (B) (C) (D)

RESONANCE 5

22. A ring of radius R is placed in the plane with its centre at origin and its axis along the x-axis and havinguniformly distributed positive charge. A ring of radius r (<< R) and coaxial with the larger ring is moving alongthe axis with constant velocity then the variation of electrical flux () passing through the smaller ring withposition will be best represented by:

(A) (B) (C) (D)

23. Eight point charges (can be assumed as small spheres uniformly charged and theircentres at the corner of the cube) having values q each are fixed at vertices of a cube.The electric flux through square surface ABCD of the cube is

(A) 024

q

(B) 012

q

(C) 06

q

(D) 08

q

24. A conducting disc of radius R rotates about its axis with an angular velocity .Then the potentialdifference between the centre of the disc and its edge is (no magnetic field is present) :

(A) zero (B) e2

Rm 22e

(C) e3

Rm 3e

(D) 2

Rme 2e

25. The negative charge �q2 is fixed while positive charge q1 as well as theconducting sphere �S� is free to move. If the system is released from rest

(A) both S and q1 move towards left(B) q1 moves towards right while S moves towards left(C) q1 remains at rest, S moves towards left(D) both q1 and S remain at rest

26. A positively charged insulator is brought near (but does not touch) two metallic sphere that are in contact.The metallic spheres are then separated. The sphere which was initially farthest from the insulator will have(A) no net charge (B) a negative charge(C) a positive charge (D) either a negative or a positive charge.


27. Two free point charges +q and +4q are placed a distance x apart. A third charge is so placed that all the threecharges are in equilibrium. Then(A) unknown charge is -4q/9(B) unknown charge is -9q/4(C) It should be at (x/3) from smaller charge between them(D) It should be placed at (2x/3) from smaller charge between them.

28. A wire having a positive uniform linear charge density , is bent in the form of a ringof radius R. Point A as shown in the figure, is in the plane of the ring but not at thecentre. Two elements of the ring of lengths a

1 and a

2 subtend very small same

angle at the point A. They are at distances r1 and r

2 from the point A respectively.

a1

a2

r2

r1

A

(A) The ratio of charge of elements a1 and a

2 is r

1/r

2.

(B) The element a1 produced greater magnitude of electric field at A than element a

2.

(C) The elements a1 and a

2 produce same potential at A.

(D) The direction of net electric field at A is towards element a2.

RESONANCE 6

COMPREHENSION

ComprehensionThe sketch below shows cross-sections of equipotential surfaces between two charged conductorsthat are shown in solid black. Some points on the equipotential surfaces near the conductors aremarked as A,B,C,........ . The arrangement lies in air. (Take

0 = 8.85 × 10�12 C2/N m2]

E

B CD

Solid conducting sphere

0.3mLarge conducting plate

�30V �20V �10V 10V 20V 30V 40V

A

( )cM+h pkyd ifêdk

( )Bksl pkyd xksyk

29. Surface charge density of the plate is equal to(A) 8.85 × 10�10 C/m2 (B) �8.85 × 10�10 C/m2

(C) 17.7 × 10�10 C/m2 (D) �17.7 × 10�10 C/m2

30. A positive charge is placed at B. When it is released :(A) no force will be exerted on it. (B) it will move towards A.(C) it will move towards C. (D) it will move towards E.

31. How much work is required to slowly move a � 1C charge from E to D ?(A) 2 × 10�5 J (B) �2 × 10�5 J (C) 4 × 10�5 J (D) �4 × 10�5 J

ASSERTION / REASON

32. Statement 1 : A positive charge particle is placed in front of a spherical uncharged conductor. Thenumber of lines of forces terminating on the sphere will be more than those emerging from it.

Statement 2 : The surface charge density at a point on the sphere nearest to the point charge will benegative and maximum in magnitude compared to other points on the sphere.(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1(C) Statement-1 is True, Statement-2 is False(D) Statement-1 is False, Statement-2 is True.

33. STATEMENT-1 : A point charge q is placed near an arbitary shaped solid conductor as shown in figure. Thepotential difference between the points A and B within the conductor remain same irrespective of the magnitudeof charge q.

q

A B

STATEMENT-2 : The electric field inside a solid conductor is zero under electrostatic conditions.(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1(C) Statement-1 is True, Statement-2 is False(D) Statement-1 is False, Statement-2 is True.

SUBJECTIVE CHOICE QUESTIONS

34. Calculate the magnitude of electrostatic force on a charge placed at a vertex of a triangular pyramid(4 vertices, 4 faces), if 4 equal point charges are placed at all four vertices of pyramid of side �a�.

RESONANCE 7

35. A rigid insulated wire frame in the form of a right angled triangle ABC, is set in avertical plane as shown. Two bead of equal masses m each and carrying chargesq1 & q2 are connected by a cord of length & slide without friction on the wires .Considering the case when the beads are stationary, determine.(a) The angle .(b) The tension in the cord &(c) The normal reaction on the beads . If the cord is now cut, what is the product of the charges for which the beads continue to remain stationary .

36. A square loop of side �� having uniform linear charge density �� is placed in �xy�

plane as shown in the figure. There is a non uniform electric field )x(a

E

i�

where a is a constant. Find the resultant electric force in µN on the loop if =10 cm,a = 2 N/C and charge density = 2µC/m.

A D

CB

y

x

37. Two infinitely long line charges having charge density each are parallel to eachother and separated by distance d. A charge particle of mass m and charge q isplaced at mid point between them. This charge is displaced slightly along a line ABwhich is perpendicular to the line charges and in the plane of the line charges. Provethat the motion of the particle will be SHM for small displacement and q > 0. Neglectgravity. Find the time period.

38. A point charge � q revolves around a fixed charge +Q in elliptical orbit. The minimum and maximum distance

of � q from Q are r1 and r2 respectively. The mass of revolving particle is m. Qq > 0 and assume no gravitationaleffects. Find the angular momentum of q about Q .

39. Find the magnitude of uniform electric field E in N/C (direction shown in figure) if anelectron entering with velocity 100m/s making 30° comes out making 60° (see

figure), after a time numerically equal to em

of electron.

40. A solid sphere of radius �R� is uniformly charged with charge density in its volume. A

spherical cavity of radius 2R

is made in the sphere as shown in the figure. Find the electric

potential at the centre of the sphere.

41. The arrangement shown consists of three elements

1. a thin rod of charge � 3.0 C that forms a full circle of radius 6.0 cm.2. a second thin rod of charge 2.0 C that forms a circular arc of radius 4.0 cm and concentric with

the full circle, subtending an angle of 90° at the centre of the full circle.

3. an electric dipole with a dipole moment that is perpendicular to a radial line and has magnitude1.28 × 10�21 C-m.

Find the net electric potential in volts at the centre.

42. Electric field in a region is given by j�y6i�x4E

. Then find the charge enclosedin the cube of side 1m oriented as shown in the diagram.

43. A conducting sphere of radius R has two spherical cavities of radius a and b. The cavities have charges qa &

qb respectively at their centres. �A� is the centre of the sphere and �B� is the centre of the cavity of radius �b�.

Find :(i) electric field & electrical potential at

(a) r (distance from A)> R,(b) r (distance from B)< b

(ii) surface charge densities on the surface of radius R, radius a & radius b.(iii) What is the force on q

a & q

b?

RESONANCE 8

MATCH THE COLUMN44. Column gives a situation in which point charge(s) are placed at different position with respect to a uncharged

thick conducting spherical shell. Column gives resulting effect. Match the figures in Column with thestatements in Column .

Column Column

(p) charge is induced on(A) q

positive point charge q is placed at

centre of shellinner surface of shell andis distributed uniformly

(q) charge is induced on inner(B) q

positive point charge q is placed inside gap of shell, but not at centre

surface of shell and is distributednon-uniformly

(r) charge is induced on outer(C)

q

positive point charge q is

placed outside the shell

surface of shell and isdistributed uniformly

(s) charge is induced on outer(D) surface of shell and is distributed

non-uniformly

ANSWERS1. C 2. C 3. A 4. A 5. A 6. A 7. D8. A 9. A 10. A 11. B 12. B 13. B 14. A15. B 16. B 17. B 18. B 19. C 20. C 21. D22. C 23. C 24. B 25. C 26. C 27. AC 28. ABCD29. A 30. B 31. D 32. D 33. A

34. 20

2

a4

q6

35. (a) 60º (b) mg + 2

21qqk

(c) 3 mg , mg . q1 & q2 should have unlike charges for the beads to remain

stationary & q1q2 =

kmg 2

36. 4 37.q4

md2 0

2

38. )rr(2

rrmqQ

210

21

39. 100 40.

0

2

12R5

41. 0 42. q = 2 0

43. (i) (a) v = r

)qq(K ba ; E = 2ba

r

)qq(K

(b) v = r

Kqb � b

Kqb + R

)qq(K ba ; E = 2b

r

Kq(ii)

R = 2

ba

R4

qq

,

a = 2

a

a4

q

,

b = 2

b

b4

q

(iii) 0

44. (A) p,r (B) q,r (C) s (D) q,s

RESONANCE 1

SINGLE CHOICE QUESTIONS1. The capacitance of a parallel plate capacitor will increase if:

(A) a battery is connected to it(B) distance between the plates is increased(C) one plate is displaced parallel to itself by distance less than its length(D) none of these.

2. A,B,C,D are large conducting plates kept parallel to each other. A andD are fixed. Plates B and C, connected to each other by a rigidconducting rod can slide over frictionless rails as shown. Initially thedistance between plates A and B is same as that between plates Cand D. If now the rod (along with plates B and C) is slightly movedtowards right, the capacitance between the terminals 1 and 2. (A) remains unchanged (B) increases(C) decreases (D) nothing can be said

3. The equivalent capacitance between x and y is:

(A)5

6 F (B)

7

6 F (C)

8

3 F (D) 4 F

4. In the figure initial status of capacitor and their connection is shown. Which of the followingis incorrect about this circuit :

(A) Final charge on each capacitor will be zero(B) Final total electrical energy of the capacitors will be zero(C) Total charge flown from A to D is 30µC

(D) Total charge flown from A to D is � 30µC

5. A parallel plate capacitor of capacitance C (without dielectrics) is filled by dielectric slabs as shown infigure. Then the new capacitance of the capacitor is:

(A) 3.9 C (B) 4 C (C) 2.4 C (D) 3 C


TOPIC : CAPACITANCE &CURRENT ELECTRICITY




RESONANCE 2

6. In the figure shown P1 and P2 are two conducting plates having charges of equalmagnitude and opposite sign. Two dielectrics of dielectric constant K1 and K2 fillthe space between the plates as shown in the figure. The ratio of electrical energyin 1st dielectric to that in the 2nd dielectric is

(A) 1 : 1 (B) K1 : K2(C) K2 : K1 (D) K2

2 : K12

7. In the circuit shown the capacitor is initially uncharged. The charge passed through an imaginarycircular loop parallel to the plates (also circular) and having the area equal to half of the area of theplates, in one time constant is:

(A) 0.63 C (B) 0.37 C (C) C

2(D) zero

8. A graph between current & time during charging of a capacitor by a battery in serieswith a resistor is shown. The graphs are drawn for two circuits. R1, R2, C1, C2 andV1V2 are the values of resistance, capacitance and EMF of the cell in the twocircuits. If only two parameters (out of resistance, capacitance, EMF) are differentin the two circuits. What is /are the correct option(s)

(A) V1 = V2; R1 > R2, C1> C2 (B) V1 > V2, R1 > R2 ; C1 = C2

(C) V1 < V2, R1< R2, C1 = C2 (D) V1 < V2, C1< C2, R1 = R2

9. In the figure a capacitor of capacitance 2µF is connected to a cell of emf 20 volt.

The plates of the capacitor are drawn apart slowly to double the distance betweenthem. The work done by the external agent on the plates is :(A) � 200 µJ (B) 200 µJ

(C) 400 µJ (D) � 400 µJ

10. The plates S and T of an uncharged parallel plate capacitor are connected across a battery. The batteryis then disconnected and the charged plates are now connected in a system as shown in the figure.The system shown is in equilibrium. All the strings and spring are insulating and massless. The magnitudeof charge on one of the capacitor plates is: [ Area of plates = A ]

(A) 0Agm2 (B) k

Agm4 0 (C) 0Agm (D) k

Agm2 0

11. In the capacitor discharge formula q = q0 e�t/ the symbol represents :(A) the time it takes for C to loose q0/e charge.

(B) the time it takes for C to loose charge q0

e1

1

(C) the time it takes for C to loose essentially all of its initial charge.(D) none of the above.

12. A uniform wire of resistance R is stretched uniformly n times & then cut to form five identicalwires. These wires are arranged as shown in the figure. The effective resistance between A & Bwill be:

(A) 5Rn

(B) 2n5

R(C)

5Rn2

(D) 2Rn2

RESONANCE 3

13. Which graph best represent the relationship between conductivity and resistivity for a solid ?

(A)

Conductivity

Res

istiv

ity(B)

Conductivity

Res

istiv

ity

(C)

Conductivity

Res

istiv

ity

(D)

Conductivity

Res

istiv

ity

14. A battery of internal resistance 2 is connected to a variable resistor whose value can vary from 4

to 10 . The resistance is initially set at 4 If the resistance is now increased then(A) power consumed by it will decrease(B) power consumed by it will increase(C) power consumed by it may increase or may decrease(D) power consumed will first increase then decrease.

15. The resistance of each arm in the circuit shown in figure has same value. (i.e. R12 =R10 = R13 = R2O = R24 = ..... etc.). The ratio Q12/Q34 of the amounts of heat liberatedper unit time in conductors 1-2 and 3-4 is :(A) 4 : 1 (B) 8 : 1 (C) 16 : 1 (D) none of these

16. In the circuit shown the variable resistance X is to be adjusted such thatthe ideal ammeter reads the same in both the positions of the key, whenconnected independently to 1 and then to 2. The reading of the ammeteris 2A. If E = 10 V, then x is : (A) 5. (B) 20

(C) 50 (D) cannot be determined

17. In the diagrams, all light bulbs are identical and all emf sources are ideal and identical. In which circuit(given in options) will each bulb glow with the same brightness as in the circuit shown ?

(A) (B) (C) (D)

18. In the circuit shown in figure, the resistance of voltmeter is 6 K. The voltmeterreading will be :

(A) 6V (B) 5V

(C) 4V (D) 3V

19. In a practical wheat stone bridge circuit as shown, when one more resistance of 100 is connected in

parallel with unknown resistance ' x ', then ratio 1/2 become ' 2 '. 1 is balance length. AB is a uniformwire. Then value of ' x ' must be:

G

1 2

E r

A B

100 x

copper strips( )rk¡cs dh ifê;k¡

copper strips( )rk¡cs dh ifê;k¡

(A) 50 (B) 100 (C) 200 (D) 400

RESONANCE 4


20. Charged particles with different charge to mass ratios are projected into the region of space betweenthe plates of a parallel plate capacitor with velocities directed parallel to the plates. All particles havereceived their initial kinetic energy by passing the same potential difference V0. The potential differenceacross the capacitor plates is V, and the distance between the plates is d. If all the particles areprojected from a point that is exactly in the middle of the distance between the plates and '' is thedistance travelled (along the direction of initial velocity) by any particle before hitting any of the plate,

then is dependent as (neglect the interaction among the particles and effect of induction) :

d

(A) 0V (B) mq

(C) V

1 (D) d

21. Two capacitors C1 & C

2 are charged to same potential V, but with opposite polarity as shown in fig.

The switch S1 & S

2 are then closed.

(A)P.d. across two capacitors are same & is given by )CC(

V)CC(

21

21

(B)P.d. across two capacitors are same & is given by )CC(

VC

21

1

(C)Ratio of final energy to initial energy of the system is

2

21

21

)CC(

)CC(

(D)Ratio of final energy to initial energy of the system is

221

1

)CC(

)C(

22. The figure shows, a graph of the current in a discharging circuit of a capacitorthrough a resistor of resistance 10 . (A) The initial potential difference across the capacitor is 100 volt.

(B) The capacitance of the capacitor is 2n101

F..

(C) The total heat produced in the circuit will be 2n

500

joules.

(D) The thermal power in the resistor will decrease with a time constant 2n2

1

second.

23. In the figure a conductor of nonuniform cross-section is shown. A steadycurrent flows in it. (A) The electric field at A is more than at B.(B) The electric field at B is more than at A.(C) The thermal power generated at A is more than at B in an element of small same width.(D) The thermal power generated at B is more than at A in an element of small same width.

RESONANCE 5

COMPREHENSIONComprehension

The circuit contains ideal battery E and other elements arranged as shown. The capacitor is initiallyuncharged and switch S is closed at t = 0. (use e2 = 7.4)

24. Time constant of the circuit is(A) 48 s (B) 28.8 s (C) 72 s (D) 120 s

25. The potential difference across the capacitor in volts, after two time constants, is approximately :(A) 2 (B) 7.6 (C) 10.4 (D) 12

26. The potential difference across resistor R1 after two time constants, is approximately :

(A) 1.6 V (B) 7.6 V (C) 10 V (D) 12 V

27. The potential difference across resistor R2 after two time constants, is :

(A) 2V (B) 7.6V (C) 10V (D) 12 V

ComprehensionIn the circuit shown below, the internal resistance of the cell is negligible. The distance of the slider from theleft-hand end of the slide wire is . The graph shows the variation with of the current in the cell.

100 cm

Slider 100 cm slider wire

� +

6.00 V d.c.

Cell Centre zero milliammeter

R

28. The balance point is at length l that is equal to(A) 0 cm (B) 20 cm (C) 30 cm (D) 40 cm

29. E.M.F. of the cell is :(A) 0.98 V (B) 1.20 V (C) 1.86 V (D) 2.00 V

ASSERTION / REASON

30. STATEMENT-1 : A dielectric is inserted between the plates of an isolated fully-charged capacitor. Thedielectric completely fills the space between the plates. The magnitude of electrostatic force on eithermetal plate decreases, as it was before the insertion of dielectric medium.STATEMENT-2 : Due to insertion of dielectric slab in an isolated parallel plate capacitor (the dielectriccompletely fills the space between the plates), the electrostatic potential energy of the capacitordecreases.(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1(C) Statement-1 is True, Statement-2 is False(D) Statement-1 is False, Statement-2 is True.

RESONANCE 6

31. STATEMENT-1 : When an external resistor of resistance R (connected across a cell of internal resistance r)is varied, power consumed by resistance R is maximum when R = r.STATEMENT-2 : Power consumed by a resistor of constant resistance R is maximum when current throughit is maximum.(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1(C) Statement-1 is True, Statement-2 is False(D) Statement-1 is False, Statement-2 is True


32. Find the equivalent capacitance between terminals �A� and �B�. The letters have their usual meaning.

33. Find the equivalent resistance of the circuit as shown in the figure between the junctions A and B. Each of thetwelve wires have a resistance R ohms .

34. (a) In the circuit shown the resistance �R� can be varied. Plot the graph of current through �R�

against R.

(b) In the figure shown �R� can be varied. Find the value of �R� so that electric power consumed

by it becomes maximum.

35. Two potentiometer wires w1 and w2 of equal length connected to a battery of emf P and internal

resistance ' r ' through two switches s1 and s2. A battery of emf is balanced on these potentiometer

wires. If potentiometer wire w1 is of resistance 2r and balancing length is /2 when only s1 is closed

and s2 is open. On closing s2 and opening s1 the balancing length on w2 is found to be

3

2, then find

the resistance of potentiometer wire w2.

RESONANCE 7

MATCH THE COLUMN

36. Column I gives physical quantities of a situation in which a current i passes through two rods I and II of equallength that are joined in series. The ratio of free electron density (n), resistivity () and cross-section area (A)of both are in ratio n

1 : n

2 = 2 : 1,

1 :

2 = 2 : 1 and A

1 : A

2 = 1 : 2 respectively. Column II gives corresponding

results. Match the ratios in Column with the values in Column .

A B C

i

Column Column

(A)

rod in electron free ofvelocity Drift rod in electron free ofvelocity Drift

(p) 0.5

(B)

rod in fieldElectric rod in fieldElectric

(q) 1

(C)

rod across difference Potential rod across difference Potential

(r) 2

(D) C to B from move to electronfreeby taken time AverageB to A from move to electron freeby taken time Average

(s) 4

37. Match the readings of the voltmeter and ammeter respectively shown in the figures.Column Column

(a) 7V24V

3

(P) 0V

(b)

7V24V

3

V

(Q) 20A

(c)

7V24V

3

(R) 0A

(d) 7V

24V

3

A (S) 20 V

RESONANCE 8

38. Column I gives certain situations in which capacitance of a capacitor is changed by different means. ColumnII gives resulting effect under different conditions. Match the statements in column I with the correspondingstatements in column II.

Column I Column II(A) The plates of a plane parallel capacitor are (p) Increases if the capacitor is maintained

slowly pulled apart. Then the magnitude of at constant charge.electric field intensity inside the capacitor.

(B) The plates of a plane parallel plate capacitor (q) Decreases if the capacitor isare slowly pulled apart. Then the potential maintained at constant chargeenergy stored in the capacitor.

(C) The capacitance of an air filled plane parallel (r) Increases if the capacitor is maintainedplate capacitor on insertion of dielectric at constant potential difference.

(D) A dielectric slab is inserted inside an air (s) Decreases if the capacitor is maintainedfilled plane parallel plate capacitor. The at constant potential difference.potential energy stored in the capacitor.

39. Two identical capacitors are connected in series, and the combination is connected with a battery, asshown. Some changes in the capacitor 1 are now made independently after the steady state is achieved,listed in column-I. Some effects which may occur in new steady state due to these changes on thecapacitor 2 are listed in column-II. Match the changes one capacitor 1 in column-I with correspondingeffect on capacitor 2 in column-II.

Cap.1 Cap.2

+ _

Column I Column II(A) A dielectric slab is inserted. (p) Charge on the capacitor increases.(B) Separation between plates increased. (q) Charge on the capacitor decreases.(C) A metal plate is inserted connecting both plates (r) Energy stored in the capacitor increases.(D) The left plate is grounded. (s) No change is occured.

ANSWERS

1. D 2. A 3. D 4. C 5. A 6. C 7. D

8. C 9. B 10. A 11. B 12. C 13. C 14. A

15. C 16. A 17. C 18. B 19. B 20. ACD 21. AC

22. ABCD 23. AC 24. A 25. C 26. A 27. D 28. B

29. B 30. D 31. B 32.d

A

1013 0 33. Req =

4R2

= 2R

34. (a) R = 0 , (b) R = 2r

35. From (1) & (2) R = r 36. (A) q (B) s (C) s (D) q

37. (a) P (b) P (c) R (d) R 38. (A) s (B) p, s (C) p, r (D) q, r 39. (A) p, r (B) q (C) p,r (D) s

RESONANCE 1


1. An electron (charge e, mass ' m ' ) is revolving around a fixed proton in circular path of radius ' r '. Themagnetic field at the centre due to electron is:

(A) 0 (B) rmr8

e

02

20

(C)

rmr8

e

0

0

(D)

rmr4

e

02

0

2. A point charge is moving in clockwise direction in a circle with constant speed. Consider the magnetic fieldproduced by the charge at a point P (not centre of the circle) on the axis of the circle.(A) it is constant in magnitude only (B) it is constant in direction only(C) it is constant in direction and magnitude both (D) it is not constant in magnitude and direction both.

3. A particle is moving with velocity j�3i�v

and it produces an electric field at a point given by k�2E

.

It will produce magnetic field at that point equal to (all quantities are in S.. units)

(A) 2c

j�2i�6 (B) 2c

j�2i�6 (C) zero (D) can not be determined from the given data

4. Two observers moving with different velocities see that a point charge produces same magnetic field at

the same point A . Their relative velocity must be parallel to r

, where r

is the position vector of point AAwith respect to point charge. This statement is :(A) true (B) false (C) nothing can be said

(D) true only if the charge is moving perpendicular to the r

5. A uniformly charged ring of radius R is rotated about its axis with constant linear speed v of each of itsparticles. The ratio of electric field to magnetic field at a point P on the axis of the ring distant x = R fromcentre of ring is (c is speed of light)

(A) v

c2(B)

cv2

(C) vc

(D) cv

6. If the magnetic field at 'P' can be written as K tan

2 then K is :

[Refer to the figure of question no. 8]

(A) d4

0

(B)

d20

(C)

d0

(D)

d

2 0


TOPIC : EMF




RESONANCE 2

7. The magnetic field at the origin due to the current flowing in the wire is

(A) )k�i�(a8

0

(B) )k�i�(

a20

(C) )k�i�(

a80

(D) )k�i�(

2a40

8. A negative charge is given to a loop and the loop is rotated in the plane ofpaper about its centre as shown. The magnetic field produced by the ringaffects a small magnet placed above the ring in the same plane of paper. (A) the magnet does not rotate(B) the magnet rotates clockwise as seen by observer from below(C) the magnet rotates anti-clockwise as seen from below(D) none of the above.

9. A nonconducting disc having uniform positive charge Q, is rotating about its axiswith uniform angular velocity . The magnetic field at the center of the disc is.

(A) directed outward (B) having magnitude R4

Q0

(C) directed inwards (D) having magnitude R2

Q0

10. A uniform circular loop of radius a and resistance R is pulled at a constant velocity v out of a region of uniform

magnetic field whose magnitude is B. The plane of loop and the velocity are both perpendicular to B

. Thenthe electrical power in the circular loop at the instant when the arc (of circular loop) outside the region of

magnetic field subtends an angle 3

at centre of the loop is :

(A) R

vaB 222

(B) R

vaB2 222

(C) R2

vaB 222

(D) None of these

11. An electron moving with velocity V along the axis approaches a circular current carrying loop as shownin the figure. The magnitude of magnetic force on electron at this instant is

(A) 2/322

20

)Rx(

xRive2

(B)

0 2/322

2

)Rx(

xRive

(C) 2/322

20

)Rx(

xRive4

(D) 0

RESONANCE 3

12. If a charged particle of charge to mass ratio mq

is entering in a magnetic field of strength B at a

speed v = (2d)(B), then which of the following is correct :

(A) angle subtended by charged particle at the centre of circular path is 2.(B) the charge will move on a circular path and will come out from magnetic field at a distance 4d

from the point of insertion.

(C) the time for which particle will be in the magnetic field is B

2

.

(D) the charged particle will subtend an angle of 900 at the centre of circular path

13. A proton moves in the positive z-direction after being accelerated from rest through a potential differenceV. The proton then passes through a region with a uniform electric field E in the positive x-direction anda uniform magnetic field B in the positive y-direction, but the proton's trajectory is not affected. If theexperiment were repeated using a potential difference of 2V, the proton would then be(A) deflected in positive x-direction (B) deflected in negative x-direction(C) deflected in positive y-direction (D) deflected in negative y-direction

14. In region x > 0, a uniform and constant magnetic field k�B2B 01

exists. Another uniform and constant

magnetic field k�BB 02

exists in region x < 0. A positively charged particle of mass m and charge q

is crossing origin at time t = 0 with a velocity i�uu 0

. The particle comes back to its initial position

after a time : (B0, u

0 are positive constants)

(A)0Bq

m23

(B) 0Bqm2

(C) 0Bqm3

(D) Particle does not come back to its initial position.

15. Figure shows an equilateral triangle ABC of side carrying currents, placed inuniform magnetic field B. The magnitude of magnetic force on triangle is :

(A) iB (B) 2 iB

(C) 3iB (D) zero

16. Two long wires which are perpendicular to each other carry currents as shown in the figure. Theyare free to move. Consider only magnetic interaction

(A) the two wires will come closer transitionally(B) the two wires will move away transitionally(C) the two wires wil l rotate such that the currents become uni-directional and then come

closer due to attraction(D) the two wires will rotate such that the currents become anti-parallel and then move far away due

to repulsion.

RESONANCE 4

17. A uniform, constant magnetic field B

is directed at an angle of 45° to the x-axis in the xy-plane, PQRS

is a rigid square wire frame carrying a steady current 0, with its centre at the origin O. At time t = 0,the frame is at rest in the position shown in the figure, with its sides parallel to the x and y axes. Eachside of the frame is of mass M and length L.

The torque

about O acting on the frame due to the magnetic field will be

(A)

= 2

LB 20 i j (B)

= 2

LB 20 j�i� (C)

= 2

LB 20 j�i� (D)

= 2

LB 20 j�i�


18. A single circular loop of wire with radius 0.02 m carries a current of 8.0 A. It is placed at the centre of asolenoid that has length 0.65 m, radius 0.080 m and 1300 turns.

Current carrying loop

Solenoid

(A) The value of the current in the solenoid so that the magnetic field at the centre of the loop becomes zero,is equal to 44 mA.(B) The value of the current in the solenoid so that the magnetic field at the centre of the loop becomes zero,is equal to 100 mA.(C) The magnitude of the total magnetic field at the centre of the loop (due to both the loop and the solenoid)if the current in the loop is reversed in direction from that needed to make the total field equal to zero tesla,is 8 x 10�5 T.(D) The magnitude of the total magnetic field at the centre of the loop (due to both the loop and the solenoid)if the current in the loop is reversed in direction from that needed to make the total field equal to zero tesla,is 16 x 10�5 T.

19. A particle of charge �q� & mass �m� enters normally (at point P) in a region of

magnetic field with speed v. It comes out normally from Q after time T as shown infigure. The magnetic field B is present only in the region of radius R and is uniform.Initial and final velocities are along radial direction and they are perpendicular toeach other. For this to happen, which of the following expression(s) is/are correct :

(A) B = qRmv

(B) T = v2R

(C) T = qB2m

(D) None of these

20. Figure shows the path of an electron in a region of uniform magnetic field. Thepath consists of two straight sections, each between a pair of uniformly chargedplates, and two half circles. The electric field exists only between the plates.

Pair-A

Pair-B

(A) Plate I of pair A is at higher potential than plate-II of the same pair.(B) Plate I of pair B is at higher potential than plate II of the same pair.

(C) Direction of the magnetic field is out of the page [ ].(D) Direction of the magnetic field in to the page [ ].

RESONANCE 5

COMPREHENSION

Comprehension

As a charged particle �q� moving with a velocity v

enters a uniform magnetic field B

, it experiences a

force F

= )( Bvq

. For = 0º or 180º, being the angle between v

and B

, force experienced is zero and

the particle passes undeflected. For = 90º, the particle moves along a circular arc and the magnetic force

(qvB) provides the necessary centripetal force

rmv2

. For other values of ( 0º, 180º, 90º), the charged

particle moves along a helical path which is the resultant motion of simultaneous circular and translationalmotions.Suppose a particle, that carries a charge of magnitude q and has a mass 4 × 10�15 kg, is moving in a region

containing a uniform magnetic field B

= � 0.4 k� T. At some instant, velocity of the particle is v

=

)�4�6�8( kji × 106 m/s and force acting on it has a magnitude 1.6 N.

21. Motion of charged particle will be along a helical path with :(A) A translational component along x-direction and a circular component in the y-z plane(B) A translational component along y-direction and a circular component in the x-z plane(C) A translational component along z-axis and a circular component in the x-y plane(D) Direction of translational component and plane of circular component are uncertain

22. Angular frequency of rotation of particle, also called the �cyclotron frequency� is :

(A) 8 × 105 rad/s (B) 12.5 × 104 rad/s (C) 6.2 × 106 rad/s (D) 4 × 107 rad/s

23. If the coordinates of the particle at t = 0 are (2 m, 1 m, 0), coordinates at a time t = 3 T, where T is the timeperiod of circular component of motion, will be (take = 3.14) :(A) (2 m, 1 m, 400 m) (B) (0.142 m, 130 m, 0)(C) (2 m, 1 m, 1.884 m) (D) (142 m, 130 m, 628 m)

ASSERTION / REASON

24. Statement 1 : A direct uniformly distributed current flows through a solid long metallic cylinder along itslength. It produces magnetic field only outside the cylinder .Statement 2 : A thin long cylindrical tube carrying uniformly distributed current along its length does notproduce a magnetic field inside it. Moreover, a solid cylinder can be supposed to be made up of many thincylindrical tubes.(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1(C) Statement-1 is True, Statement-2 is False(D) Statement-1 is False, Statement-2 is True

25. STATEMENT-1 : A pendulum made of an insulated rigid massless rod of length is attached to a smallsphere of mass m and charge q. The pendulum is undergoing oscillations of small amplitude having time

period T. Now a uniform horizontal magnetic field B

out of plane of page is switched on. As a result of thischange, the time period of oscillations does not change.

STATEMENT-2 : A force acting along the string on the bob of a simple pendulum (such that tension in stringis never zero) does not produce any restoring torque on the bob about the hinge.(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1(C) Statement-1 is True, Statement-2 is False(D) Statement-1 is False, Statement-2 is True

RESONANCE 6

26. STATEMENT�1 : No electric current will be present within a region having uniform and constant magneticfield.

STATEMENT�2 : Within a region of uniform and constant magnetic field B

, the path integral of

magnetic field

dB along any closed path is zero. Hence from Ampere circuital law IodB

(where the given terms have usual meaning), no current can be present within a region havinguniform and constant magnetic field.(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1(C) Statement-1 is True, Statement-2 is False(D) Statement-1 is False, Statement-2 is True.


27. A thin beam of charged particles is incident normally on the boundary of a region containing a uniformmagnetic field as shown. The beam comprise of monoenergetic and � particles, each possessing akinetic energy T. Neglecting interaction between particles of the beam, find the separation between the and particles when they emerge out of the magnetic field. (express your answer in terms of T, B, e, me & m

,

where all terms have their usual meanings.) (Te T )

28. The given fig. shows a coil bent with AB = BC = CD = DE = EF = FG = GH = HA = 1 m and carrying current1 A. There exists in space a vertical uniform magnetic field of 2 T in the y-direction. Then find out the torque(in vector form) on the loop.

MATCH THE COLUMN

29. A beam consisting of four types of ions A, B, C and D enters a region that contains a uniform magneticfield as shown. The field is perpendicular to the plane of the paper, but its precise direction is not given.All ions in the beam travel with the same speed. The table below gives the masses and charges of theions.

Ion beam

r1r2r4 r3

Region containingMagnetic field

21 43

r > r = r > r4 3 2 1

ION MASS CHARGEA 2m eB 4m � e

C 2m � e

D m + e

RESONANCE 7

The ions fall at different positions 1, 2, 3 and 4, as shown. Correctly match the ions with respectivefalling positions.

Column Column

(a) A (P) 1

(b) B (Q) 2

(c) C (R) 3

(d) D (S) 4

30. A charged particle having non zero velocity is subjected to certain conditions given in Column . Column gives possible trajectories of the particle. Match the conditions in column with the results in Coulmn

Column Column

(A) In only uniform electric field (p) the path of the charged particle maybe a straight line

(B) In only uniform magnetic field (q) the path of the charged particle maybe a parabola

(C) In uniform magnetic and uniform electric field (r) the path of the charged particle maysuch that both are parallel be a circle

(D) Subjected to a net force of constant magnitude (s) the path of the charged particle maybe a helix with uniform or non uniform pitch

31. A uniform and constant magnetic field exists in whole space as shown by magnetic lines of forces.Each of the four particles 1, 2, 3 and 4 have charge +q and mass m. Each of the particle is given ainitial velocity of magnitude 'v

'; the angle between initial velocity of each particle and magnetic field is

shown (velocity of particle 2 is along the magnetic field and velocity of particle 4 is perpendicular tomagnetic field). Neglect electrostatic and magnetic force on each charge due to remaining threecharges. Match the statements in column-I with particle(s) they correspond to in column-II.

Column-I Column-II

(A) The magnitude of angle between velocity (p) Particle 1and magnetic field does not change for

(B) Total distance travelled in time 't' is equal (q) Particle 2to 'vt

' for

(C) The magnitude of acceleration is (r) Particle 3non zero and constant for

(D) If a uniform electric field is switched on in (s) Particle 4direction of existing magnetic field, thename of the path of trajectory becomes different for

RESONANCE 8

32. A square wire frame ABCD is made of four thin uniform rods of length 'a' each. The charge per unitlength on each of four rods is uniform and . The frame moves in x-y plane (z = 0 plane) with constant

velocity i�vv 0

, the centre of frame always lies on x-axis and side BC is parallel to y-axis. At the

instant centre of frame is at origin, match the positions in column- with respective nature of fields incolumn-II.

Column-I Column-II

(A) At point P whose coordinates are (4a, 0, 0) (p) magnitude of magnetic field is zero

(B) At point Q whose coordinates are (0, 4a, 0) (q) magnitude of magnetic field is nonzero

(C) At point R whose coordinates are (0, 0, 4a) (r) magnitude of electrostatic field is zero

(D) At origin (s) magnitude of electrostatic field is nonzero

ANSWERS

1. B 2. A 3. A 4. A 5. A 6. B 7. C

8. B 9. AD 10. A 11. D 12. B 13. B 14. B

15. A 16. C 17. A 18. BD 19. ABC 20. ABC 21. C

22. D 23. C 24. D 25. A 26. A

27.eB

T22

em

2

m28. 2 k� units 29. (a) S (b) P (c) Q (d) R

30. (A) p, q ; (B) p, r, s ; (C) p, s ; (D) p, q, r, s 31. (A) p,q,r,s, (b) p,q,r,s, (c) p,r,s (d) s

32. (A) p,s (B) q,s (C) q,s (D) p,r

revision test physics

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