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प्रश्न
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.
उत्तर
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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