General Science • PhysicsHard

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

A. The hollow spherical shell reaches the bottom first because of its lighter core.

B. The solid uniform sphere reaches the bottom first because it possesses a smaller moment of inertia coefficient.✓ Correct Answer

C. Both objects reach the bottom at the exact same time because gravitational acceleration is independent of mass and geometry.

D. The hollow spherical shell reaches the bottom first because a greater fraction of its mass is concentrated at the periphery.

💡 Solution & Explanation

When an object rolls down an incline without slipping, its potential energy converts into both translational and rotational kinetic energy. The solid sphere has a lower moment of inertia relative to its mass than the hollow shell, meaning less energy is partitioned into rotation and more goes into translational speed, allowing it to accelerate faster and finish first. Moment of inertia measures an object resistance to angular acceleration about an axis of rotation.

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

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