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A block slides down from top of a smooth inclined plane of elevation $θ$ fixed in an elevator going up with an acceleration $a_{0}$ . The base of incline has length L. Find the time taken by the block to reach the bottom.

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${[\frac{4 L}{(g - a_{0}) \sin 2 θ}]}^{\frac{1}{2}}$

${[\frac{4 L}{(g - a_{0}) \sin θ}]}^{\frac{1}{2}}$

${[\frac{4 L}{(g + a_{0}) \sin θ}]}^{\frac{1}{2}}$

${[\frac{4 L}{(g + a_{0}) \sin 2 θ}]}^{\frac{1}{2}}$

answer is A.

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Detailed Solution

net force acting on the body w.r.t lift

$m (g + a_{0})$

$acceleration along the plane (g + a_{0}) sinθ$

length of the plane s=L/cos $θ$

$t i m e t a k e n t = \sqrt{\frac{2 s}{a}} = \sqrt{\frac{2 L 2}{2 \cos θ (g + a_{0}) \sin θ}}$

$t = \sqrt{\frac{4 L}{(g + a_{0}) \sin 2 θ}}$

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