Torques of equal magnitude are applied to a hollow cylinder and a solid sphere, both having the same mass and radius. The cylinder is free to rotate about its standard axis of symmetry, and the sphere is free to rotate about an axis passing through its centre. The angular velocity of the solid sphere is:

A child stands at the centre of a turntable with his arms outstretched. The turntable is set to rotate with an angular speed of \(40\) rev/min. How much is the angular speed of the child if he folds his hands back and thereby reduces his moment of inertia to \(2\over 5\) times the initial value?
1. \(160\) rev/min
2. \(150\) rev/min
3. \(100\) rev/min
4. \(120\) rev/min

A man stands on a rotating platform, with his arms stretched horizontally holding a \(5~\text{kg} \) weight in each hand. The angular speed of the platform is \(30\) revolutions per minute. The man then brings his arms close to his body with the distance of each weight from the axis changing from \(90~\text{cm}\) to \(20~\text{cm}.\) The moment of inertia of the man together with the platform may be taken to be constant and equal to \( 7.6~\text{kg}~\text{m}^2.\) What is his new angular speed?
1. \(60~\text{rev/min}\)
2. \(57.0~\text{rev/min}\)
3. \(58.8~\text{rev/min}\)
4. \(60.1~\text{rev/min}\)

A bullet of mass \(10\) g and speed \(500\) m/s is fired into a door and gets embedded exactly at the center of the door. The door is \(1.0\) m wide and weighs \(12\) kg. It is hinged at one end and rotates about a vertical axis practically without friction. The angular speed of the door just after the bullet embeds into it is:
1. \(0.122\) rad/s
2. \(0.625\) rad/s
3. \(0.231\) rad/s
4. \(0.191\) rad/s