Question

Torques of equal magnitude are applied to hollow cylinder and a solid sphere, both having the same mass and same 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

Let M be the mass and R the radius of the hollow cylinder, and also of the solid sphere. Their moments of inertia about the respective axes are `l_(1) =MR^(2) " and " l_(2)=2//5 MR^(2)`
Let T be the magnitude of the torque applied to the cylinder and the sphere, producing angular accelerations `alpha_(1) " and " alpha_(2)` respectively. Then `T=l_(1) alpha_(1)=l_(2) alpha_(2)`
The angular acceleration 04 produced in the sphere is larger. Hence, the sphere will acquire larger angular speed after a given time.