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Question: A solid sphere of mass m and radius R falls vertically on fixed smooth inclined plane with a speed u...

A solid sphere of mass m and radius R falls vertically on fixed smooth inclined plane with a speed u. Find the angle θ if after the collision, the sphere moves horizontally. Coefficient of restitution between the sphere and the inclined plane is e.

A

sin–1 e

B

tan–1 e

C

tan⁡−1e\tan^{- 1}\sqrt{e}

D

cos⁡−1e\cos^{- 1}\sqrt{e}

Answer

tan⁡−1e\tan^{- 1}\sqrt{e}

Explanation

Solution

Let initial velocity be u and final velocity be v

v cos θ = u sin θ ...................(1)

(∵\becauseinclined plane is smooth)

and, vsin⁡θ−0−ucos⁡θ−0=−e\frac{v\sin\theta - 0}{- u\cos\theta - 0} = - e ............(2)

⇒ e = tan2 θ or θ - tan⁡−1e\tan^{- 1}\sqrt{e}