Question

A block is kept on a frictionless inclined surface with angle of inclination $\alpha$. The inclined wedge is given an acceleration $a$ to keep the block stationary with respect to the inclined plane. Then magnitude of acceleration $a$ is equal to

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

Answer 1

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

Analysing from inclined surface frame, FBD of block is

For block to remain stationary,
$mg\sin \alpha =ma\cos \alpha$
$\Rightarrow a=g\tan \alpha$
The correct option is (D)