A solid metal sphere and a hollow metal sphere of identical outer radius and same mass are allowed to roll down an inclined plane from rest without slipping. Which sphere reaches the bottom of the inclined plane first?

💡 Solution & Explanation

The acceleration of an object rolling down an inclined plane depends inversely on its moment of inertia relative to its mass and radius squared. A solid sphere has a smaller moment of inertia compared to a hollow sphere of the same mass and radius, meaning less energy is partitioned into rotational kinetic energy and more goes into translational motion. Consequently, the solid sphere accelerates faster and reaches the bottom first. The moment of inertia of a solid sphere is two-fifths of mass times radius squared.