a-2 lm-sol

8/10/2019 A-2 LM-SOL

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A – 2 LAWS OF MOTION

1.

The system is pushed by a force F as shown in figure. All surfaces are smooth except between B and

friction coefficient between B and C is μ. Minimum value of F to prevent block B from downw

slipping is

(a)3

2mg

(b)5

2mg

(c)5

2

mg (d)3

2

mg

KEY: b

SOL:

2.

Two blocks of mass 4 kg and 2 kg are connected by a heavy string and placed on rough horizan

plane. The 2 kg block is pulled with a constant force F. the coefficient of friction between the blo

and the ground is 0.5. What is the value of F so that tension in the string is constant throughout du

the motion of the blocks ?

( g = 10 m /s2 )

(a) 40 N (b) 30 N (c) 50 N (d) 60 N

KEY: b

SOL:

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3.

Two beads A nad B of equal mass m are connected by a light inextensible cord. They are constrainto move on a frictionless ring in vertical plane. The blocksare released from rest as shown in fig

The tension in the cord just after the release is

(a)4

mg (b) 2 mg (c)2

mg (d)2

mg

KEY: d

SOL:

4.

A car is moving in a circular horizantal track of radius 10 m with a constant speed of 10 m/s. A plu

bob is suspended from the roof of the car by a light rigid rod . The angle made by the rod with

vertical is ( g = 10 m/s2 )

(a) zero (b) 300 (c) 45

0 (d) 60

0

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Key: c

Sol:

5.

Three balls each of mass 1 kg are attached with three strings each of length 1m as shown in figThey are rotated in a horizantal circle with angular velocity ω = 4 rad/s about point O. Match

following

Table 1 Table 2

( A ) T1 ( P ) Maximum

( B ) T2 ( Q ) Minimum

( C ) T3 ( R ) 80 N

( S ) 45 N

( T ) 90 N

Key:

Sol:

8/10/2019 A-2 LM-SOL


Concept : If a string is attached with a block, then it can only pull the block, it can’t push the block.

6.

A block of mass m is attached with a massless instretchable string. Breaking strength of string is 4 m

Block is moving up. The maximum acceleration and maximum retardation of the block can be

(a) 4g, 3g (b) 4g, g (c) 3g, g (d) 3g, 4g

Key: c

Sol:

Concept : If a mass m is moving in a circle of radius R with angular velocity ω then a centripetal force mRω

required towards the centre which is provided by the available forces, for example friction, tension etc.

7. Two blocks of mass 1 kg and 2 kg are joined by a massless inextensible string of length 3 m. Both blo

are kept on a horizantal table as shown. Friction coefficient between 2 kg block and table is zero. They

rotated about a vertical axis passing at a distance of 1 m from 1 kg. Force of friction on 1 kg is (assu

that there is enough friction between 1 kg block and ground )

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(a) 12 N towards centre

(b) 20 N towards centre

(c) 20 N away from the centre

(d) 12 N away from the centre

Key: d

Sol:

8. A body is supported on a range plane including at 300 to the horizontally by a string attached to the b

and held at an angle of 300 to the plane. Draw a diagram showing the forces acting on the body and reso

each of these forces:

(a)

Horizontally and vertically,

(b)

Parallel and perpendicular to the plane.

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9. A rod AB rests with the end A on rough horizontal ground and the end B against a smooth vertical wall. T

rod is uniform and of weight W. If the rod is in equilibrium in the position shown in fig. find:

(a)

Frictional force at A

(b)

Normal reaction at A

(c)

Normal reaction at B

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10. One end of a string 0.5 m long if fixed to a point A and the other end is fastened to a small object of we

8 N. The object is pulled asaid by a horizontal force F, until it is 0.3 m from the vertical through A. Find t

magnitude of the tension T in the string and the force F.

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11. A point A on a sphere of weight W rests in contact with a smooth vertical wall and is supported by a

string joining a point B on the sphere to a point C on the wall. Draw free body diagram of the sphere.

Key:

Sol:

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12. Two beads of equal masses m are attached by a string of length 2a and free to move in a smo

circular ring lying in a vertical plane as shown fig. Here, a is the radius of the ring. Find the tension a

acceleration of B just after the beads are released to move.

Key:

Sol:

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13. Two blocks of mass 4 kg and 2 kg are placed side by side on a smooth horizontal surface as shown in fig. A horizontal force of side 20 N applied on 4 kg block. Find:-

(a)

The acceleration of each block

(b)

The normal reaction between two blocks.

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14. Three blocks of mass 3 kg, 2 kg and 1 kg are placed side by side on a smooth surface as shown fig

horizontal force of 12 N is applied on 3 kg block. Find the net force on 2 kg block.

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15. In the arrangement shown in fig. The strings are light and inextensible. The surface over which blocks

placed is smooth. Find :

(a)

The acceleration of each block,

(b)

The tension in each string.

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16. Two blocks of mass 4 kg and 2 kg are attached by an inextensible light string as shown fig. Both the blo

are pulled vertically upwards by a force F=120N find:

(a)

The acceleration of the blocks

(b)

Tension in the string. (Take g=10 m/s2).

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17. Three blocks of mass 1 kg, 4 kg and 2 kg are placed on a smooth horizontal plane as shown fig. Find:

(a)

The acceleration of the system(b)

The normal force between 1 kg block and 4 kg block,

(c)

The net force on 2 kg block.

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Sol:

18. Two blocks of mass 2 kg and 4 kg are released from rest over a smooth inclined plane of inclination 30

shown fig. What is the normal force between the two blocks?

Sol:

19. What should be the acceleration ‘a’ of the box shown in fig so that the block of mass m exerts a forcem

on the floor of the box?

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Sol:

20. A plumb bob of mass 1 kg is hung from the ceiling of a train compartment. The train moves on an incli

plane with constant velocity. If the angle of incline is 300, find the angle made by the string with the norma

the ceiling. Also, the tension in the string.(g=10m/s2)

Sol:

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21. Repeat both parts of the above question, if the train moves with an acceleration a=2

g up the plane.

Sol:

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22. Two blocks of mass 1kg and 2 kg are connected by a string AB of mass 1 kg. The blocks are placed o

smooth horizontal surface. Block of mass 1 kg is pulled by a horizontal force F of magnitude 8 N. Find

tension in the string at points A and B.

Sol:

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23. In the system shown in fig pulley is smooth. String is massless and inextensible. Find acceleration of

system a, tensions1T and

2T .(g=10 m/s

2)

24. In the system shown in fig all surfaces are smooth. String is massless and inextensible. Find acceleratio

of the system and tension T in the string. (g=10 m/s2)

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Sol:

25. In the adjacent figure, mass of A, B and C are 1 kg, 3 kg and 2 kg respectively. Find :

(a)

The acceleration of the system and

(b)

Tension in the string.

Neglect friction. (g=10 m/s2)

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a-2 lm-sol

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