Question

A solid sphere rolls down two different inclined planes of the same heights but different angles of inclination. In each case, the ball will reach the bottom _____________

(a) With the same speed

(b) With different speed

(c) With different speed but same time

(d) Immediately

I had been asked this question during a job interview.

The doubt is from Angular Momentum in portion System of Particles and Rotational Motion of Engineering Physics I

Answer 1

Right option is (a) With the same speed

Explanation: Acceleration of the rolling sphere,

a=gsinθ/((1+k^2/R^2))

Velocity of the sphere at the bottom of the inclined plane,

v=√(2gh/((1+k^2/R^2)))

The sphere will reach the bottom with the same speed v because h is the same in both the cases.