Question

In the figure shown, if a ball of mass $m$ is at rest relative to the wedge moving to the left with an acceleration $a=g\sqrt{3}$, find the force exerted by the vertical face of the wedge on mass $m$.

• A. $\frac{2mg}{\sqrt{3}}$
• B. $mg\sqrt{3}$
• C. $\frac{4mg}{\sqrt{3}}$
• D. $\frac{\sqrt{3}mg}{4}$

Answer 1

The correct option is C $\frac{4mg}{\sqrt{3}}$

Using pseudo force concept
In the frame of reference of the wedge, the mass $m$ has no acceleration.
The force exerted by verticle face on $m$ is the normal force $N_1$
From FBD of the sphere we have

$\therefore N_1=ma+N_2\cos 60°$
and, $N_2\sin 60°=mg$
$\Rightarrow N_2=mg\frac{2}{\sqrt{3}}$
$\Rightarrow N_1=mg\sqrt{3}+\frac{2mg}{\sqrt{3}}\left(\frac{1}{2}\right)=\frac{4mg}{\sqrt{3}}$