A solid sphere, disc and solid cylinder all of the same mass and made of the same material are allowed to roll down (from rest) on the inclined plane, then

A solid sphere, disc, and solid cylinder of the same material and mass are allowed to roll down an inclined plane from rest. They will have different motions because their moments of inertia are different. The moment of inertia is a measure of how mass is distributed relative to the axis of rotation. Among the three shapes, the solid sphere has the smallest moment of inertia in proportion to its mass; hence, the sphere will accelerate faster than the other two down the incline.

As the shapes roll down the slope, they convert gravitational potential energy into kinetic energy. The solid sphere, with its advantageous distribution of mass, will reach the bottom first, followed by the disc. The disc’s moment of inertia is greater than that of the sphere but smaller than that of the solid cylinder, which means it will accelerate more quickly than the cylinder but not as quickly as the sphere.

The solid cylinder, having the largest moment of inertia, will experience the slowest acceleration and therefore will arrive at the bottom of the incline last. Thus, the solid sphere wins the race down the incline, followed by the disc and then the cylinder.

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