Question

A smooth inclined plane of angle of inclination ${30}^o$ is placed on the floor of a compartment of a train moving with a constant acceleration $a$. When a block is placed on the inclined plane, it does not slide down or up the plane. The acceleration $a$ must be:

• A. $g$
• B. $\frac{g}{2}$
• C. $\frac{g}{\sqrt{2}}$
• D. $\frac{g}{\sqrt{3}}$

Answer 1

The correct option is D $\frac{g}{\sqrt{3}}$

From FBD as shown in figure, the block will not slide down or up if $ma\cos 30=mg\sin 30$.

Thus, $a=g\tan 30=g\left(\frac{1}{\sqrt{3}}\right)$