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.

Answer 1

M.I of the cylinder = I1 = MR2

and M.I. of the sphere = I2 = 2/5 MR2

Angular acceleration of the cylinder,

α1 = τ/I1 = {τ}/{MR2}

Angular acceleration of the sphere,

α2 = τ/I2 = {τ}/{2/5 MR2} = {2.5 τ}/{MR2} = 2.5 α1

It is clear that the sphere will acquire a greater angular acceleration.