Question

A block is kept on a frictionless inclined surface with angle of inclination $\alpha$. The incline is given an acceleration $a$ to keep the block stationary. Then $a$ is equal to (Take acceleration due to gravity $=g$)

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

Answer 1

The correct option is D $g\tan \alpha$

In the reference frame of the wedge, pseudo force $ma$ acts towards right and component of this $ma$ is $ma\cos \alpha$ balances the $mg\sin \alpha$.
$mg\sin \alpha =ma\cos \alpha$
$\Rightarrow a=g\tan \alpha$