Question

A box when dropped from a certain height reaches the ground with a speed ν. When it slides from rest from the same height down a rough inclined plane inclined at an angle 45° to the horizontal, it reaches the ground with a speed ν/3. The coefficient of sliding friction between the box and the plane is (acceleration due to gravity is 10 ms^–2) 

(A) 8/9

(B) 1/9

(C) 2/3

(D) 1/3 

Answer 1

Correct option (A) 8/9

Explanation:

When box is dropped from a height h, then speed at ground is v, therefore using mechanical energy conservation 

 

when body slides on rough inclined plane, friction force will also act f = μN = μ mg cosθ Applying work-energy theorem