Question

A block of mass is resting on a wedge of angle $\theta$ with what minimum acceleration ${}^{\prime }{a}^{\prime }$ should the wedge move so that the mass falls freely ?

• A. $g=a\sin \theta$
• B. $ma\sin \theta$
• C. $m(g+a)\sin \theta$
• D. $m(g-a)\sin \theta$

Answer 1

The correct option is A $g=a\sin \theta$

REF.Image

To have free fall motion, the block should loose the contact with wedge.

$\therefore asin\theta \ge gcos\theta$

$\therefore a=gcot\theta ........\left(1\right)$

Motion along incline :

$a^{\prime }=gsin\theta +acos\theta$

$=gsin\theta +gcot\theta .cos\theta$

$=g[sin\theta +\frac{co{s}^2\theta }{sin\theta }]$

$=g\left[\frac{1}{sin\theta }\right]$

$\therefore a^{\prime }sin\theta =g$

Acceleration in vertically downward direction is g.