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.

Explanation

If M is mass and R is radius of the hollow cylinder and the solid sphere, then
M.I of hollow cylinder about its axis of symmetry `I_(1)=MR^(2)` and
M.I of solid sphere about an axis through its centre, `I_(2)=(2)/(5)MR^(2)`
Torque applied, `I=I_(1)alpha_(1)=I_(2)alpha_(2)`
`(alpha_(2))/(alpha_(1))=(I_(1))/(I_(2))=(MR^(2))/((2)/(5)MR^(2))=(5)/(2)`
`alpha_(2)gtalpha_(1)`
From `omega=omega_(0)+alphat`, we find that for given `omega_(0)` and t, `omega_(2)gtomega_(1)` i.e. angular speed of solid sphere will be greater than angular speed of hallow sphere.