Question

An object is kept on a smooth inclined plane of height 1 unit and length $l$ units. The horizontal acceleration to be imparted to the inclined plane so that the object is stationary relative to the incline is given by

• 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

The correct option is C

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

Given AB = 1, AC = l, so that $BC=\sqrt{l^2-1}$.
Thus, $tan\theta =\frac{AB}{BC}=\frac{1}{\sqrt{l^2-1}}$.
A horizontal acceleration a imparted to the inclined plane has a component $acos\theta$ down the plane. If this equals the component $gsin\theta$ along the plane, the object will appear stationary relative to the incline.
$acos\theta =gsin\theta$
$\Rightarrow a=gtan\theta =\frac{g}{\sqrt{l^2-1}}$
Hence, the correct choice is (c).