Question

A hollow sphere, a solid sphere, a disc and a ring all having same mass and radius are rolled down on an inclined plane. If no slipping takes place, which one will take the smallest time to cover a given length?

Answer 1

Answer with Explanation ⇒

According to the question, each object has the same radius, thus the total torque on each of them will be same. Thus, the angular acceleration will be given by the 

Formula :-

                  α =Γ/I.

Thus from this relation we can say that the object with minimum 'I' will be having the maximum angular acceleration.

Now, Let us see the value of 'I' for the given objects ⇒

Hollow sphere = (2/3)mr²

Solid Sphere = (2/5)mr²

Disc = 1/2 mr²

Ring = mr²

From this we can observes that the minimum 'I' of them is for the solid sphere. Thus, the solid sphere will take the smallest time to cover a given length.

Hope it helps.