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The Principle

A sphere of m...

Question

A sphere of mass, $m$ is held at a height of $2 R$ between a wedge of same mass $m$ and a rigid wall, is released from rest. Assuming that all the surfaces are frictionless. Find the speed of both the bodies when the sphere hits the ground.

v_{w} = \sqrt{2 g R} cos α, v_{s} = \sqrt{2 g R} sin α

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v_{w} = \sqrt{2 g R} sin α, v_{s} = \sqrt{2 g R} cos α

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v_{w} = \sqrt{2 g R} cos α, v_{s} = \sqrt{2 g R} cos α

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v_{w} = \sqrt{2 g R} sin α, v_{s} = \sqrt{2 g R} sin α

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Solution

The correct option is A $v_{w} = \sqrt{2 g R} cos α, v_{s} = \sqrt{2 g R} sin α$
$C o n s e r v a t i o n o f e n e r g y g i v e s \frac{1}{2} m {v_{w}}^{2} + \frac{1}{2} m {v_{s}}^{2} = m g R t a n α = \frac{v_{s}}{v_{w}} \Rightarrow v_{w} = \sqrt{2 g R} c o s α a n d v_{s} = \sqrt{2 g R} s i n α$

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