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 \( g \) for the block to remain stationary on the wedge is
\includegraphics[width=0.5\linewidth]7.png

• A. \( a = \frac{g}{\sec \theta} \)
• B. \( a = \frac{g}{\sin \theta} \)
• C. \( a = g \tan \theta \)
• D. \( a = g \cos \theta \)

Hint:

When a block is stationary on an inclined plane with a moving wedge, the acceleration of the wedge must balance the component of gravitational force acting on the block.

Answer 1

The Correct Option is B

Step 1: Understand the forces acting on the block.
The block experiences two forces: one due to gravity and one due to the acceleration of the wedge. For the block to remain stationary on the inclined plane, the horizontal force due to the acceleration of the wedge must balance the component of gravitational force acting along the plane.
Step 2: Set up the force balance equation.
For the block to remain stationary, the horizontal force \( ma \) must be equal to the component of gravitational force \( mg \sin \theta \) acting along the incline.
Step 3: Solve for \( a \).
\[ ma = mg \sin \theta \] \[ a = g \sin \theta \] Final Answer: \[ \boxed{a = \frac{g}{\sin \theta}} \]