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 sphere about its axis = \(\frac{2}{5}\)MR²

M.I. of hollow cylinder about its axis = MR²

Since torque to both bodies are the same

τ  = 1 α ⇒ α = \(\frac {τ}{1}\) 

Hence the object with lesser M.I. will have a higher angular acceleration and hence higher angular speeds at any moment. Thus the sphere will have higher angular speeds after a given time.