Question

A hollow sphere and a solid sphere having same mass and same radii are rolled down a rough inclined plane.
(a) The hollow sphere reaches the bottom first.
(b) The solid sphere reaches the bottom with greater speed.
(c) The solid sphere reaches the bottom with greater kinetic energy.
(d) The two spheres will reach the bottom with same linear momentum.

Answer 1

(b) The solid sphere reaches the bottom with greater speed.

Explanation: 

For a hollow sphere, the linear acceleration 

a = (3/5)g.sinθ = 0.60g.sinθ 

For solid sphere a = (5/7)g.sinθ = 0.71g.sinθ 

Since 'a' for solid sphere is more so it will reach the bottom with a greater speed. 

Since both the spheres are released from the same position, their initial potential energy mgh will be the same. So when they reach the bottom they lose same amount of P.E. and this loss of P.E. will be the gain in K.E. So both the spheres will have same K.E.at the bottom. Option (c) is not correct. 

Since the solid sphere reaches the bottom with a greater speed and both have same mass, they can not have the same linear momentum. Thus option (d) is not correct.