Question

Two balls are dropped from same height h, one on a smooth plane and the other on a rough plane having same inclination θ with horizontal as shown in figure. Both the planes have same coefficient of the restitution. If range and time of flight of first and second balls are R₁, T₁ and R₂, T₂ respectively, then:

• A. T₁ = T₂, R₁ = R₂
• B. T₁< T₂, R₁< R₂
• C. T₁ = T₂, R₁> R₂
• D. T₁> T₂, R₁> R₂

Answer 1

Answer: (A)

T₁ = T₂, R₁ = R₂

Answer 2

The velocity of the ball just before striking the plane = $\sqrt{2gh}$

Velocity resolved into two components

(i) $\sqrt{2gh}$ cos θ, normal to the plane, and

(ii) $\sqrt{2gh}$sin θ, parallel to the plane.

Since the ball is not rotating therefore, its surface does not have tendency to slide over th rough planes during collision.

Hence, friction does not come into existence. And Both the balls will have same velocity along the same direction. Therefore T₁ = T₂ and R₁ = R₂.

Hence, (1) is the correct choice