Q: A smooth inclined plane of length L having inclination θ with the horizontal is inside a lift which is moving down with a retardation *a*. The time taken by a body to slide down the inclined plane from rest will be.

(a) $\displaystyle \sqrt {\frac{2L}{(g+a)sin\theta}} $

(b) $\displaystyle \sqrt {\frac{2L}{(g-a)sin\theta}} $

(c) $ \displaystyle \sqrt {\frac{2L}{a sin\theta}} $

(d) $ \displaystyle \sqrt {\frac{2L}{g sin\theta}} $

Ans: (a)

Sol:

$ \displaystyle L = \frac{1}{2}(g+a)sin\theta \times t^2$

$ \displaystyle t = \sqrt{\frac{2L}{(g+a)sin\theta}}$