Three objects of uniform density- a solid sphere, a solid cylinder, and a hollow cylinder- are placed at the top of an incline. they are all released from rest at the same elevation and roll without slipping. which object reaches the bottom first? which reaches it last? try this at home and note that the result is independent of the masses and the radii of the objects.

Explanation:

Given

three objects namely Solid sphere, Solid cylinder and hollow cylinder are released from same elevation

Suppose all have same mass and radius

acceleration of object and while rolling

Moment of inertia of Solid sphere

Moment of inertia of Solid cylinder

Moment of inertia of Hollow cylinder

therefore

Distance traveled is same so

time is inversely Proportional to square root of acceleration

time Period of solid sphere

where k holds for other constant terms

so time taken by Solid sphere is least and last one to reach at bottom is solid cylinder