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 ${}^{\prime }{a}^{\prime }$ 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 $\theta$