question_answer

An object is kept on a smooth inclined plane of 1 in \[l\]. The horizontal acceleration to be imparted to the inclined plane so that object is stationary relative to the incline is given by

A) \[g({{l}^{2}}-1)\]

B) \[g({{l}^{2}}-1)\]

C) \[\frac{g}{\sqrt{{{l}^{2}}-1}}\]

D) \[\frac{g}{{{l}^{2}}-l}\]

Correct Answer: C

Solution :

[c]

The situation is as shown in the in the figure

\[\tan \theta =\frac{1}{\sqrt{{{t}^{2}}-1}}\]

The free body diagram of block is shown in the below figure.

For equilibrium of block w.r.t. incline,\[mg\,\sin \theta =ma\,\cos \theta \]

\[\Rightarrow \]   \[a=g\,\tan \theta =\frac{g}{\sqrt{{{l}^{2}}-1}}\]