Question

A block of mass $m$ is placed on a smooth inclined wedge $ABC$ of inclination $\theta$ as shown in the figure. The wedge is given an acceleration $'a'$ towards the right. The relation between $a$ and $\theta$ for the block to remain stationary on the wedge is

• A. $a = g \, \tan \, \theta$
• B. $a = \frac{g}{cosec \, \theta}$
• C. $a = g \, \cos \, \theta$
• D. $a = \frac{g}{\sin \, \theta}$

Answer 1

Answer: (A)

In non-inertial frame,
$N$ sin $\theta$ = ma ....(i)
$N$ cos $\theta$ = mg ...(ii)
$\tan \, \theta = \frac{a}{g}$
$a = g$ tan $\theta$