The horizontal acceleration that should be given to a smooth inclined plane of angle $\sin ^{-1}\left(\frac{1}{l}\right)$ to keep an object stationary on the plane, relative to the inclined plane is :

• Correct answer
  A

  $\frac{g}{\sqrt{l^2-1}}$
• B

  $g \sqrt{l^2-1}$
• C

  $\frac{\sqrt{l^2-1}}{g}$
• D

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

Solution

Let horizontal acceleration given is $a$
Horizontal force $=m a \cos \theta$ $\therefore m a \cos \theta=m g \sin \theta$ $a=g \tan \theta$ $=\frac{g}{\sqrt{l^2-1}}$

Hence, the correct answer is option: 'A'.