Laws of Motion

In the given arrangement of a doubly inclined plane two blocks of masses M and m are placed. The blocks are connected by a light string passing over an ideal pulley as shown. The coefficient of friction between the surface of the plane and the blocks is 0.25. The value of m, for which M=10 kg will move down with an acceleration of 2 m/s2, is: (take g=10 m/s2 and 37 =3/4) [figure]

1. 4.5 kg
2. 6.5 kg
3. 9 kg
4. 2.25 kg

An artillery piece of mass M1 fires a shell of mass M2 horizontally. Instantaneously after the firing, the ratio of kinetic energy of the artillery and that of the shell is:

1. M1/(M1+M2)
2. M2M1
3. M1M2
4. M2/(M1+M2)

A coin is placed on a disc. The coefficient of friction between the coin and the disc is . If the distance of the coin from the center of the disc is r, the maximum angular velocity which can be given to the disc, so that the coin does not slip away, is :

1. r g
2. gr
3. gr
4. rg

[figure] A block of mass 5 kg is placed on a rough inclined surface as shown in the figure. If F1 is the force required to just move the block up the inclined plane and F2 is the force required to just prevent the block from sliding down, then the value of | F1 |- | F2 | is : [Use g=10 m/s2]

1. 25 3 N
2. 50 3 N
3. 5 32 N
4. 10 N

A light string passing over a smooth light fixed pulley connects two blocks of masses m1 and m2. If the acceleration of the system is g/8, then the ratio of masses is: [figure]

1. 81
2. 97
3. 53
4. 43

All surfaces shown in figure are assumed to be frictionless and the pulleys and the string are light. The acceleration of the block of mass 2 kg is : [figure]

1. g2
2. g4
3. g
4. g3

A spherical body of mass 100 g is dropped from a height of 10 m from the ground. After hitting the ground, the body rebounds to a height of 5 m. The impulse of force imparted by the ground to the body is given by : (given, g=9.8 m/s2)

1. 43.2 kg ms-1
2. 2.39 kg ms-1
3. 4.32 kg ms-1
4. 23.9 kg ms-1

A block of mass m is placed on a surface having vertical cross-section given by y=x2/4. If coefficient of friction is 0.5, the maximum height above the ground at which block can be placed without slipping is:

1. 1/2 m
2. 1/3 m
3. 1/6 m
4. 1/4 m

Three blocks A, B and C are pulled on a horizontal smooth surface by a force of 80 N as shown in figure [figure] The tensions T1 and T2 in the string are respectively :

1. 40N, 64N
2. 60N, 80N
3. 80N, 100N
4. 88N, 96N

If the radius of curvature of the path of two particles of same mass are in the ratio 3:4, then in order to have constant centripetal force, their velocities will be in the ratio of :

1. 1: 3
2. 2: 3
3. 3:2
4. 3:1