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. $R=mg,a=g$
• B. $R=mg,a=\sqrt{2}g$
• C. $R=2mg,a=g$
• D. $R=2mg,a=\sqrt{2}g$

Answer 1

The correct option is B $R=mg,a=\sqrt{2}g$

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

So, $R=ma=mg$

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 $a_{net}=\sqrt{2}g$

Hence option B is the correct answer.