Question

A body slides down a smooth iniclined plane of inclincation 30° , vertical height, h. It starts from rest from the top and accquires a speed v₁ on reaching the bottom of inclined plane. The body is recast in the shape of a uniform disc. The disc starts from rest from top of an identical rough inclined plane (μ = 0.2) as before. It rolls down without slipping. It accquires a linear speed v₂ as it reaches the bottom of the inclined plane v²/v¹ is

(1) 1

(2) √2/3

(3) √2/5

(4) √2/7

Answer 1

(2) √2/3

The acceleration of body down smooth inclined plane is g sin θ . The speed v₁ is

v₁ = √2gh ....(i)

Let a be the linear acceleration of C.M of circular disc as it rolls down the inclined plane. Then

The speed, v₂ as it reaches the bottom of inclined plane is