Question

A block is sliding along inclined plane as shown in figure. If the acceleration of chamber is $a$, as shown in the figure. The time required to cover a distance $L$ along incline is:

• A. $\sqrt{\frac{2L}{g\sin \theta -a\cos \theta }}$
• B. $\sqrt{\frac{2L}{g\sin \theta +a\sin \theta }}$
• C. $\sqrt{\frac{2L}{g\sin \theta +a\cos \theta }}$
• D. $\sqrt{\frac{2L}{g\sin \theta }}$

Answer 1

Answer: (C)

$\sqrt{\frac{2L}{g\sin \theta +a\cos \theta }}$

Applying pseudo force $ma$ along left direction of the block.

The net acceleration along the incline will be $a_{effective}=a\cos \theta +g\sin \theta$

The time required will be $L=0\times t+\frac{1}{2}{a}_{effective}{t}^2$

$\Rightarrow \sqrt{\frac{2L}{a_{effective}}}$

$\Rightarrow \sqrt{\frac{2L}{a\cos \theta +g\sin \theta }}$