Question

With what acceleration ‘$a$’ should the box in the figure descend so that the block of mass $M$ exerts a force $Mg/4$ on the floor of the box?

• A. $g/4$
• B. $g/2$
• C. $3g/4$
• D. $4g$

Answer 1

The correct option is C $3g/4$

Free body diagram of block is as shown, by the non-inertial frame of refrence there will be pseudo force acting on the block of magnitude $Ma$ in the upward direction as the box accelerates downward,

Where $N$ is the normal on the block by the box and the same force will be applied by the block on the box
$N=F=M(g-a)$, it is given that the force exerted is $\frac{Mg}{4}$, substituting the value in the above equation we get

$\frac{Mg}{4}=M(g-a)$

$Ma=Mg-\frac{Mg}{4}$
$a=\frac{3g}{4}$
Hence option (c) is the correct answer.