Equal torques are applied on a cylinder and a hollow sphere. Both have same mass and radius. The cylinder rotates about its axis and the sphere rotates about one of its diameters. Which will acquire greater speed ? Explain.

Explanation

From `tau = I alpha or alpha = (tau)/(I)`
As `tau = constant, alpha prop (1)/(I) :. (alpha_(c))/(alpha_(s)) = (I_(s))/(I_(c))`
Now moment of inertia of cylinder about its axis
is `I_(c) = (1)/(2)MR^(2)`
and moment of inertia of hollow sphere about its diameter is
`I_(s) = (2)/(3)MR^(2)`
`:. (alpha_(c))/(alpha_(s)) = (2//3MR^(2))/(1//2MR^(2)) = (4)/(3) :. alpha_(c) gt alpha_(s)`
Hence, the cylinder will acquire greater speed compared to the hollow sphere.