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)

$\frac{g}{\sqrt{l^{2}-1}}$

Answer 2

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