Question

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

The correct option is C $\sqrt{\frac{2L}{g\sin \theta +a\cos \theta }}$

Acceleration of block is,
$a=g\sin \theta +a\cos \theta$ ... (1)
From equation of motion,
$l=\frac{1}{2}\text{(acceleration)}{t}^2$

$\therefore t=\sqrt{\frac{2l}{\text{acceleration}}}$
$\therefore t=\sqrt{\frac{2l}{g\sin \theta +a\cos \theta }}$ (from (1))