Question

The horizontal acceleration that should be given to a smooth inclined plane of angle $si{n}^{-1}\left(\frac{1}{l}\right)$ to keep an object stationary on the plane, relative to the inclined plane is

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

Answer 1

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

To keep body stationary, forces must balance along inclination plane.

So, $macos\theta =mgsin\theta$

So, $a=gtan\theta$

Since, $\theta =si{n}^{-1}\left(\frac{1}{l}\right)\Rightarrow tan\theta =\frac{1}{\sqrt{l^2-1}}$

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