Question

A rectangular box is sliding on a smooth inclined plane of inclination $\alpha$ as shown in the figure. At t = 0, the box starts to move on the inclined plane. A bolt starts to fall from point A. Find the time after which bolt strikes the bottom surface of the box.

• A. $\sqrt{\frac{l}{gcos\alpha }}$
• B. $\sqrt{\frac{l}{gsin\alpha }}$
• C. $\sqrt{\frac{2l}{gcos\alpha }}$
• D. $\sqrt{\frac{2l}{gsin\alpha }}$

Answer 1

The correct option is C $\sqrt{\frac{2l}{gcos\alpha }}$

As chamber slides down the inclined one, component of weight will make bolt to fall down straight because bolt will also have acceleration, along inclined plane same as chamber.

Let time taken be $t$.

$s=ut+\frac{1}{2}a{t}^2$

$t=\sqrt{\frac{2s}{g_{effective}}}$

$t=\sqrt{\frac{2\times l}{g\cos \alpha }}$