Question

A block is kept on a frictionless inclined surface with angle of inclination $\alpha$ as shown in figure. The incline is given an acceleration $a$ to keep the block stationary. Then $a$ is equal to

• A. $g\tan \alpha$
• B. $g$
• C. $gcosec\alpha$
• D. $\frac{g}{\tan \alpha }$

Answer 1

Answer: (A)

The incline is given an acceleration $a$. Acceleration of the block is to the right. Pseudo acceleration $a$ acts on the block to the left. As it is clear from figure, the block will remain stationary, when
$ma\cos \alpha =mg\sin \alpha$ or $a=\frac{g\sin \alpha }{\cos \alpha }=g\tan \alpha$