Question
A solid sphere and a hollow sphere both roll down from the same point from the same inclined plane without slipping. Which of the two spheres reach the ground earlier and with greater speed?
Solution
Rotational inertia for solid sphere = 
Rotational Inertia for hollow sphere =
Kinetic energy is due to both rotational as well as translational motion. But, here the rotational motion of solid sphere is less than the hollow sphere. This implies the translational component of solid will be higher. Hence, the solid sphere will move down with a greater velocity.
Rotational Inertia for hollow sphere =
Kinetic energy is due to both rotational as well as translational motion. But, here the rotational motion of solid sphere is less than the hollow sphere. This implies the translational component of solid will be higher. Hence, the solid sphere will move down with a greater velocity.
