Question

In figure shown, all surfaces are smooth. A force $F=2mg$ is acting on block $A$. If $R$ is contact force between $A$ and $B$ and $a$ is acceleration of $B$, then

• A. $a=g$
• B. $a=\sqrt{g}$
• C. $a=\sqrt{2}g$
• D. $a=\sqrt{3}g$

Answer 1

The correct option is C $a=\sqrt{2}g$

We know that, acceleration of combined mass $a_c=\frac{F}{2m}=\frac{2mg}{2m}=g$
Now for the reaction force $\left(R\right)$, we draw the free body diagram of the block.


So, $R=m{a}_c=mg$

Now for the acceleration of the block $B$, it will have vertical acceleration $=g$ and horizontal acceleration we got as $g$

So, the net acceleration will be $a_{net}=a=\sqrt{2}g$

Hence option B is the correct answer.