Question

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

• A. $\frac{g}{\sqrt{l^2-1}}$
• B. $g\sqrt{l^2-1}$
• C. $\frac{g\sqrt{l^2-1}}{l}$
• D. $\frac{g}{\sqrt{l^2+1}}$

Answer 1

The correct option is A $\frac{g}{\sqrt{l^2-1}}$



Writing the equations in the frame of the incline plane.
Balancing forces along the incline,
$mg\sin \theta =ma\cos \theta$
$\Rightarrow g\left(\frac{1}{l}\right)=a\cos \theta$
$\Rightarrow a=\frac{g}{l\cos \theta }$
$\Rightarrow a=\frac{g}{l\left(\frac{\sqrt{l^2-1}}{l}\right)}=\frac{g}{\sqrt{l^2-1}}$