Q. 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 the inclined is
A) $g\sqrt{l^{2} - 1}$
B) $g(l^{2} -$1)
C) $\frac{g}{\sqrt{l^{2} - 1}}\ \ $
D) $\frac{g}{l^{2} - 1}$
Explanation
(c) $Here,\ \ \sin{\theta = \frac{1}{l}}$
Let required acceleration of inclined plane be a for the object to remain stationary relative to incline, we have
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$ma\cos{\theta =}mg\sin\theta$
$a = g\tan{\theta = g\frac{1}{\sqrt{l^{2} - 1}}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.