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 the object is stationary relative to incline is

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

B)  \[g({{l}^{2}}-1)\]

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

D)         \[\frac{g}{{{l}^{2}}-1}\]

Correct Answer: C

Solution :

Here,\[\sin \theta =\frac{1}{l}\] When horizontal acceleration is imparted to the inclined plane, [hen a pseudo acceleration acts on the object. For the object to remain stationary relative to the incline, we have                 \[a=g\tan \theta =g\frac{1}{\sqrt{{{l}^{2}}-1}}\] or            \[a=\frac{g}{\sqrt{{{l}^{2}}-1}}\]