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 :

• 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 $\frac{g}{\sqrt{l^2-1}}$

The above figure shows a body that is kept one smooth inclined plane of inclined $1$ in $x$.

Let the inclined angle is $\theta$

$sin\theta =\frac{1}{l}$

$\tan \theta =\frac{1}{\sqrt{x^2-l}}$

Now see the above free body diagram

$ma\cos \theta =mg\sin \theta$

$a=g\tan \theta$

Put $tan\theta =\frac{1}{\sqrt{r^2-l}}$

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