Consider a uniform solid sphere and a hollow spherical shell of identical mass and outer radius rolling down an inclined plane without slipping from rest simultaneously. Which object reaches the bottom of the incline first?

💡 Solution & Explanation

When objects roll down an incline without slipping, gravitational potential energy converts into both translational and rotational kinetic energy. The solid sphere possesses a smaller moment of inertia relative to its mass compared to the hollow spherical shell, meaning less energy is partitioned into rotation and more goes into linear acceleration down the slope. Plausible distractors incorrectly assume mass or outer radius alone determines descent speed or neglect rotational dynamics. The moment of inertia for a solid sphere is two-fifths mass times radius squared whereas for a thin spherical shell it is two-thirds.