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Question
A block A can slide on a frictionless incline of angle θ and length l, kept inside an elevator going up with uniform velocity v in the following figure. Find the time taken by the block to slide down the length of the incline if it is released from the top of the incline.
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Solution
The force on the block which makes the body move down the plane is the component of its weight parallel to the inclined surface.
F = mg sinθ
Acceleration, g = sin θ
Initial velocity of block, u = 0
Distance to be covered
s = l
a = g sin θ
Using, \[s = ut + \frac{1}{2}a t^2\]
\[l = 0 + \frac{1}{2}\left( g\sin\theta \right) t^2 \]
\[ \Rightarrow t^2 = \frac{2l}{g\sin\theta}\]
\[ \Rightarrow \text{ Time taken }, t ={\sqrt{\frac{2l}{gsin\theta}}}\]
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