Question

Find the acceleration of wedge towards right so that friction does not act on the block.

• A. $\frac{g}{\sqrt{3}}$
• B. $\sqrt{3}g$
• C. $\frac{\sqrt{3}g}{2}$
• D. zero

Answer 1

The correct option is A $\frac{g}{\sqrt{3}}$

For no friction force there should be no relative motion between wedge and the block.
So relative to the wedge, the component of the pseudo force along the slope acting on the block must balance the component of gravitational force along the slope.
Pseudo Force is $ma$, where $a$ is the acceleration of wedge.
$\therefore macos\theta -mgsin\theta =0\Rightarrow a=gtan{30}^0=\frac{g}{\sqrt{3}}$