Question

A body on a smooth inclined plane inclination 1 in $x(sin\theta =1/x)$ will remain stationary relative to the inclined plane if the plane is given a horizontal acceleration equal to:

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

Answer 1

The correct option is D $\frac{g}{\sqrt{x^2-1}}$

From free body diagram,

$macos\theta =mgsin\theta$

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

Given, $sin\theta =\frac{1}{x}$

$cos\theta =\sqrt{1-si{n}^2\theta }=\frac{\sqrt{x^2-1}}{x}$

$tan\theta =\frac{1}{\sqrt{x^2-1}}$. . . . . .(2)

Put equation (2) in equation (1), we get

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

The correct option is D.