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. $a = \frac{g}{\text{coses} \theta}$
• B. $a = \frac{g}{\sin \theta}$
• C. $a = g \tan \theta$
• D. $a = g \cos \theta$

Answer 1

Answer: (C)

Apply Pseudo force in Non-Inertial Frame.
Apply Newton's Second Law of Motion.
Stepl: Draw free body diagram
Free body diagram is drawn in Non-Inertial Frame. Non inertial frame is accelerated
frame that is wedge.
So Pseudo force(ma) acts in opposite direction of acceleration of frame.

Step2:Apply Newton's Second Law of motion
In non-inertial frame, Block is at rest with respect to wedge so net force along incline is zero.
$\Rightarrow m a \cos \theta=m g \sin \theta$
$\Rightarrow a=g \tan \theta$