Same torque is applied on a solid cylinder and solid sphere with same mass and radius. Cylinder rotates about its axis and sphere about its diameter. Then in a given time, the angular velocity acquired is

A solid sphere and a hollow cylinder with the same mass and radius are subjected to equal torques. 

We know torque is

$\mathrm{\tau }=\mathrm{I\alpha }$

$\Rightarrow \mathrm{\alpha }\propto \frac{1}{\mathrm{I}}$

The value of moment of inertia will be lower for a sphere than a cylinder for same values of mass and radius.

That implies angular acceleration will be more for sphere and so does the angular velocity attained in a given time.