Question

An object is kept on a smooth inclined plane of inclination ${\sin }^{-1}\left(\frac{1}{L}\right)$ can be kept stationary relative to the incline by giving a horizontal acceleration of ______

• A. $\frac{g}{L^2-1}$ to the inclined plane
• B. $\frac{g}{L^2+1}$ to the inclined plane
• C. $\frac{g}{\sqrt{L^2-1}}$ to the inclined plane
• D. $\frac{g}{\sqrt{L^2+1}}$ to the inclined plane

Answer 1

Answer: (C)

$\frac{g}{\sqrt{L^2-1}}$ to the inclined plane

The free body diagram for the question as seen from inclined plane frame of reference is shown in the attached figure.

Now the component of psuedo force on the block along the inclined plane should balance the acceleration of block due to gravity down the plane.

So $mgsin\theta =macos\theta$

$a=gtan\theta$ ...(1)

Given $sin\theta =\frac{1}{L}$

$⟹tan\theta =\frac{1}{\sqrt{L^2-1}}$

Putting this in equation 1, we get

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