Question

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

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

Answer 1

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

If the mass of block is $m$,
And forces are acting on in it are in equilibrium state then it is in stationary, because both forces cancel out each other.
i.e.,
$ma\cos \alpha =mg\sin \alpha$
Hence,
$a=g\tan \alpha$

Final answer: (b)