A solid sphere is rotating about a diameter at an angular velocity w.w. If it cools so that its radius reduces to1n1n of its original value, its angular velocity becomes
1. wnwn
2. wn2wn2
3. nwnw
4. n2wn2w
A horizontal platform is rotating with uniform angular velocity around the vertical axis passing through its centre. At some instant of time a viscous fluid of mass 'm' is dropped at the centre and is allowed to spread out and finally fall. The angular velocity during this period
1. Decreases continuously
2. Decreases initially and increases again
3. Remains unaltered
4. Increases continuously
For L=3.0 m,L=3.0 m, the total torque about pivot AA provided by the forces as shown in the figure is:
1. | 210 Nm210 Nm | 2. | 140 Nm140 Nm |
3. | 95 Nm95 Nm | 4. | 75 Nm75 Nm |
For the same total mass, which of the following will have the largest moment of inertia about an axis passing through the centre of gravity and perpendicular to the plane of the body?
1. A disc of radius aa
2. a ring of radius aa
3. a square lamina of side 2a2a
4. four rods forming square of side 2a2a
The radius of gyration of a uniform rod of length LL about an axis passing through its centre of mass is
1. L2√3L2√3
2. L212L212
3. L√3
4. L√2
If the kinetic energy of a body increases by 0.1%, the percent increase of its momentum will be
1. 0.05%
2. 0.1%
3. 1.0%
4. 10%
A solid cylinder and a hollow cylinder, both of the same mass and same external diameter are released from the same height at the same time on an inclined plane. Both roll down without slipping. Which one will reach the bottom first?
1. Both together only when the angle of inclination of the plane is 450
2. Both together
3. Hollow cylinder
4. Solid cylinder
A man is sitting on a rotating table with his arms stretched outwards. When he suddenly folds his arms inside, then
1. his angular velocity will decrease
2. his angular velocity remains constant
3. his moment of inertia decreases
4. angular momentum increases