Question

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

• A. $\sqrt{\frac{2L}{g \sin \theta}}$
• B. $\sqrt{\frac{2L}{\alpha \sin \theta}}$
• C. $\sqrt{\frac{2L}{(g + \alpha) \sin \theta}}$
• D. $\sqrt{\frac{2L}{(g - \alpha) \sin \theta}}$

Hint:

When solving for time on a moving lift, always consider the effective acceleration due to gravity and retardation.

Answer 1

The Correct Option is C

In the moving lift, the effective acceleration is $(g + \alpha) \sin \theta$, so the time taken for the body to slide down is given by: \[ t = \sqrt{\frac{2L}{(g + \alpha) \sin \theta}} \]