Q.
A body of mass $m$ is resting on a wedge of angle $\theta$ as shown in figure. The wedge is given at acceleration $\alpha$. What is the value of a son that the mass $m$ just falls freely?
A) $g$
B) $g\sin\theta$
C) $g\tan\theta$
D) $g\cot\theta$
Explanation
(d) The horizontal acceleration $a$ of the wedge should be such that in time the wedge moves the horizontal distance $BC$. The body must fall through a vertical distance $AB$ under gravity. Hence,
$BC = \frac{1}{2}at^{2}$ and $AB = \frac{1}{2}gt^{2}$
tan$\theta = \frac{AB}{BC} = \frac{g}{a}\ $or $a = \frac{g}{tan\theta} = g\ cot\theta$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.