Question

A smooth inclined plane of inclined length $l$ and unit vertical length , has a particle on its inclined surface. The horizontal acceleration to be given to the inclined plane so that the particle remains stationary relative to the inclined surface, must be :

• A. $\frac{g}{\sqrt{l^2-1}}$
• B. $\frac{\sqrt{l^2-1}}{g}$
• C. $g\sqrt{l^2-1}$
• D. $g\sqrt{l^2+1}$

Answer 1

The correct option is A $\frac{g}{\sqrt{l^2-1}}$

Let $\theta$ be the angle the incline forms with the horizontal.
Hence, $tan\theta =\frac{1}{\sqrt{l^2-1}}$

For the particle to remain stationary with respect to block, the net force acting on particle down along the plane must be equal to the pseudo force it experiences upwards.

Hence, $mgsin\theta =macos\theta$

$\Rightarrow a=g\tan \theta$ $=\frac{g}{\sqrt{l^2-1}}$