work - power & energy and centre of mass

8/8/2019 Work - Power & Energy and Centre of Mass

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Mohammed

Asif

Name :

Roll No. :

Topic :

Ph : 9391326657,

64606657

WORK POWER & ENERGY AND CENTRE OF MASSCONSERVATION OF MOMENTUM, COLLISIONS

SECTION I

I. This section contains 9 multiple choice questions numbered 1 to9. Each question has 4 choice (A), (B), (C), and (D), out of whichOnly One is correct.

1. A particle of mass m is kept at the edge of a smooth cube of mass M andside L as shown in figure. Cube starts moving at t = 0 with a constantvelocity v. Displacement of the center of mass along the horizontaldirection from t = 0 to when particle hits the ground is

M

mv

s m o

A) mv L 2Lm M v g

+ +

B) mv v 2Lm M L g

+ +

C)Mv L 2L

m M v g

+

+ D)

Mv v 2L

m M L g

+

+

2. There are two masses 1 2M and M placed at a distance l apart, Let the centre

of mass of this system is at a point named C. If 1 1M is displaced l towards C

and 2 2M is displacedby l away from C. The distance from C where the new

centre of mass will be located is

A)2 1 1 2

1 2

M l M l

M M

++ B)

1 1 2 2

1 2

M l M l

M M

++

C)1 1 2 2

1 2

M l M l

M M

+ C)2 1 1 2

1 2

M l M l

M M

+

3. In a boat of mass 4M and length L on a frictionless water surface. Twomen A(mass = M) B( mass = 2M) are standing on the opposite ends. Now Atravels a distance L/4 relative to boat towards its centre and B moves a

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distance 3L/4 relative to boat and meet A. The displacement of he boat onwater till A and B meet is

A)5L

28B) zero C)

L

2D)

23L

24. A paraboloid shaped solid object is formed byrotating on

parabola y = 2x2 about y axis as shown in

figure. If theheight of the body is h then the position of

centre of massfrom origin. (Assume density to be uniform

throughout).

A)h

3B)

h

4 C)

2h

3D)

2h

4

O

Y

h

x

5. A pendulum of mass m and length 1 isreleased from

rest in a horizontal position. A nail at adistance d belowthe pivot causes the mass to move to along

the path asindicated by dotted lines. Find the minimum

distance din terms of l such that the mass will swing

completelyround in the circle shown

m

d

l

A)2

lB)

3

4

lC)

3

5

lD)

2

3l

6. A particle of mass m and speed v collides elasticallywith the end

of a free uniform thin rod of mass M in a horizontalplane as

shown. After the collision, m is stationary. CalculateM.

A) m B) 2m C) 3m D)4m

M

m

v ( T o p v i )

7. Two small balls A and B of mass M and 3M respectively hang from the

ceiling by ideal strings of equal lengths. The A ball is drawn aside so that itis raised to a height H. If the ball A is released and collides with ball B;Select the correct answer (s).

A) If collision is perfectly elastic, ball B will rise to aheight H/4

B) If the collision is perfectly elastic ball A will rise uptoa height H/4

C) If the collision is perfectly inelastic, the combinedmass will rise to a height H/16

D) If the collision is perfectly inelastic, the combined

A

BH




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mass will rise to a height H/4

8. There are two observers A and B, observer Ais fixed to

the smooth plank and observer B isstanding on

smooth horizontal ground. The plank is

acceleratedwith constant acceleration, and C is placed

on it then

BC

mA

a

s m o o t h

p l a n k s m o

A) Momentum of block C is conserved as seen by observer A

B) Momentum of block C is conserved as seen by observer B

C) Net force on plank is zero as seen by observer AD) Net force on plank is non-zero as seen by observer B

9. The figure shows two blocks of mass 2 kgand 1 kg

accelerating at 4 m/s2 and 8 m/s2respectively

starting from rest as shown in the figure,then which

of the following are true at any instant(before the

collision).

2 k g 1 k g4 m / s2 8 m / s

2

s m o o

A) aCM 0= B) vCM 0C) position of centre of mass is constant D) position of centre of mass is

not constant

SECTION IIAssertion Reason Type

I. This section contains 4 questions numbered 10 to 13. Each questioncontains STATEMENT 1

(Assertion) and STATEMENT 2 (Reason). Each question has 4 choices(A), (B), (C) and (D),

out of which ONLY ONE is correct.NOTE: -

A. Statement 1 is True, Statement 2 is True; Statement 2 is a correctexplanation forStatement 1.

B. Statement 1 is True, Statement 2 is True; Statement 2 is NOT a correctexplanation for

Statement 1.C. Statement 1 is True, Statement 2 is False.D. Statement 1 is False, Statement 2 is True.




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10. A rod is in contact with a wedge which is kept on theground and can move only along its length betweenrigid supports as shown. If all the surfaces aresmooth and the system is released from rest, then

STATEMENT 1: - The mechanical energy of the system during the

motion will beconserved.

STATEMENT 2: - The momentum of the system along horizontaldirection is not

conserved.

11. STATEMENT 1: - The centre of mass of a system of particles isindependent of coordinate

system.STATEMENT 2: - The centre of mass of system of two particles always

divides the linejoining them in the inverse ratio of their masses.

12. STATEMENT 1: - On the application of impulse, the body will alwaysmove along the

direction of the impulse.STATEMENT 2: - Change in momentum is always along the direction of

impulse.

13. STATEMENT 1: - Kinetic energy of a system can be increased withoutapplying any

external force on the system.STATEMENT 2: - Single external force acting on a particle necessarilychanges its

kinetic energy.

SECTION IIILinked Comprehension Type

I. This section contains 2 paragraphs P14-16 , and P17-19 . Based uponeach paragraph, 3 Multiple choice questions have to beanswered. Each question has 4 choices (A), (B), (C), and (D), out of

which Only One is correct.

P14 - 16 : Paragraph for Questions Nos. 14 to 16

A light inextensible thread passes over a smallfrictionless ideal

pulley. Two blocks of masses m = 1 kg and M = 3 kgrespectively

are attached with the thread as shown in the figure.The heavier

block rests on a horizontal surface. A shell of mass 1

m

M

A

3 00




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kg movingupward, parallel to incline, with a velocity 10 ms-1

collides at t = 0and sticks to m. The combined mass travels up the

incline to adistance s, stops for a moment and then moves down

the incline.

When the moving mass reaches its initial position, the string becomes tautand the mass M starts to climb up with an initial speed v0. The mass Mmoves up to a height h before stopping momentarily. The inclined plane issmooth and along. The acceleration due to gravity is g = 10 m/s2 Answerthe following questions:

14. The value of s is:A) 1. 5 m B) 2. 0 m C) 2. 5 m D) 1. 0 m

15. The value of v0 is:A) 1. 0 m/s B) 2. 0 m/s C) 2. 5 m/s D) 5. 0 m/s

16. The value of h is:A) 0. 5 m B) 1. 0 m C) 2. 0 m D) 2. 5 m

P17 - 19 : Paragraph for Questions Nos. 17 to 19

A circular platform of mass 100 kg is placed symmetrically on a squareframe of side 4m having four legs. The radius of the platform is 5m.

17. The maximum permissible mass of a dancer so that the platform does not

topple isA) 33. 3 kg B) 66. 7 kg C) 50 kg D) 75 kg

18. The area on the platform on which any mass of the dancer is permissible isA) 16 m2 B) 78. 5 m2 C) 8 m2 D) 62. 5 m2

19. If five dancers are there on the stage each of mass 40 kg then themaximum number of dancer that can go together at same position alongthe circumference of the stage with the remaining staying at the centre sothat the platform does not topple isA) 1 B) 2 C) 3 D) 4

SECTION IVMatrix Match Type




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This section contains 3 questions. Each question containsstatement given in two columns which have to be matched.Statement (A, B, C, D) in Column I have to be matched withstatements (p, q, r, s) in Column II. The answers to thesequestions have to be appropriately bubbled as illustrated inthe following example. If the correct matches are A-p, A-s, B-q, B-r, C-p, C-q and D-s, then the correctly bubbled 4 X4

matrix should be follows:

A

B

C

D

p q r s

20. When a body is moving vertically up with constant velocity under the actionof a lifting force and air resistance is absent.

21. A ball strikes the ground at an angle and rebound atan angle with the vertical as shown in figure. Thenmatch the column I with column II from thecombinations shown:

22. Match the Column I with Column II



Column - I Column - IIA Work done by lifting force (p) NegativeB Total work done by all the

forces(q) Positive

C Work done by gravity (r) ZeroD If air resistance starts

acting then work done byair resistance if it actsopposite to motion.

(s) Non zero

Column - I Column - IIA Elastic collision (p)

( )tan

tan

B Perfectly inelastic collision (q) 0, 90

work - power & energy and centre of mass

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