Question

An object is kept on a smooth inclined plane of $1 $ in $ l. $ The horizontal acceleration to be imparted to the inclined plane so that the object is stationary relative to incline is

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

Answer 1

Answer: (C)

Here, $\sin \theta=\frac{1}{l}$
When horizontal acceleration is imparted to the inclined plane, then a pseudo acceleration acts on the object. For the object to remain stationary relative to the incline, we have

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