Question
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. Which of the two will acquire a greater angular speed after a given time?
Solution
Torque is given by,
And using the equation of motion for rotational motion, 
So, on two different bodies, if the same torque is applied for the same time, the body, which has a smaller moment of inertia, acquires greater angular speed.
We know that the moment of inertia of sphere is less than that of the hollow cylinder.
Therefore, the solid sphere will acquire greater angular speed.
