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Question: A particle is projected on a frictionless inclined plane of inclination 37<sup>0</sup> from the hori...

A particle is projected on a frictionless inclined plane of inclination 370 from the horizontal , with the projection angle 450 from the inclined plane as shown in the figure. After one collision from the plane, it reaches to its initial point of projection. Coefficient of restitution between particle and plane is-

A

23\frac{2}{3}

B

13\frac{1}{3}

C

325\frac{3}{25}

D

12\frac{1}{\sqrt{2}}

Answer

325\frac{3}{25}

Explanation

Solution

While going upward

R = 2u2sin⁡αcos⁡(α−β)cos⁡2β\frac{2u^{2}\sin\alpha\cos(\alpha - \beta)}{\cos^{2}\beta}

while going down ward

R = 2u2sin⁡αcos⁡(α+β)cos⁡2β\frac{2u^{2}\sin\alpha\cos(\alpha + \beta)}{\cos^{2}\beta}