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 (figure 5−E22). 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.

Answer 1

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, $s=ut+\frac{1}{2}a{t}^2$, we get:
$$\begin{gathered} l=0+\frac{1}{2}\left(g\sin \theta \right)t^2 \\ \Rightarrow t^2=\frac{2l}{g\sin \theta } \\ \Rightarrow \mathrm{Time}\mathrm{taken},t=\sqrt{\frac{2\mathrm{l}}{\mathrm{gsin}\theta }} \end{gathered}$$