System of Particles and Rotational Motion

A solid sphere of radius 4 cm and mass 5 kg is rotating (rotation axis is passing through the centre of the sphere) with an angular velocity of 1200 rpm. It is brought to rest in 10 s by applying a constant torque. The torque applied and the number of rotations it made before it comes to rest are and respectively.

1. 0.128 Nm, 100
2. 0.0128 Nm, 50
3. 0.128 Nm, 50
4. 0.0128 Nm, 100

A wheel initially at rest is subjected to a uniform angular acceleration about its axis. In the first 2 s it rotates through an angle 1 and in the next 2 s it rotates through an angle 2. The ratio 2 1 is .

1. 6
2. 3
3. 4
4. 13

Two masses 400 g and 350 g are suspended from the ends of a light string passing over a heavy pulley of radius 2 cm. When released from rest the heavier mass is observed to fall 81 cm in 9 s. The rotational inertia of the pulley is kg m2. (g = 9.8 m/s2)

1. 8.3 10-3
2. 4.75 10-3
3. 1.86 10-2
4. 9.5 10-3

A thin uniform rod (X) of mass M and length L is pivoted at a height ( L3 ) as shown in the figure. The rod is allowed to fall from a vertical position and lie horizontally on the table. The angular velocity of this rod when it hits the table top, is . (g = gravitational acceleration) [figure]

1. 32 gL
2. 3gL
3. 3 2 gL
4. 1 2 gL

A uniform rod of mass m and length l is suspended by means of two identical inextensible light strings as shown in figure. Tension in one string immediately after the other string is cut, is . (g acceleration due to gravity) [figure]

1. mg/3
2. mg/4
3. mg
4. mg/2

The pulley shown in figure is made using a thin rim and two rods of length equal to diameter of the rim. The rim and each rod have a mass of M. Two blocks of mass of M and m are attached to two ends of a light string passing over the pulley, which is hinged to rotate freely in vertical plane about its center. The magnitude of the acceleration experienced by the blocks is (assume no slipping of string on pulley). [figure]

1. (M - m)g [ ( 83 )M + m ]
2. (M - m)g2M + m
3. (M - m)gM + m
4. (M - m)g [ ( 136 )M + m ]

A cord of negligible mass is wound around the rim of a wheel supported by spokes with negligible mass. The mass of wheel is 10 kg and radius is 10 cm and it can freely rotate without any friction. Initially the wheel is at rest. If a steady pull of 20 N is applied on the cord, the angular velocity of the wheel, after the cord is unwound by 1 m, would be: [figure]

1. 20 rad/s
2. 30 rad/s
3. 10 rad/s
4. 0 rad/s