A block of mass $$M$$ placed inside a box descends vertically with acceleration $$a$$. The block exerts a force equal to one-fourth of its weight on the floor of the box. The value of '$$a$$' will be

A block of mass $$M$$ inside a box descends vertically with acceleration $$a$$. The block exerts a force equal to one-fourth of its weight on the floor.

When the system descends with acceleration $$a$$, the apparent weight (normal force $$N$$) is:

$$N = M(g - a)$$

The block exerts a force $$N = \frac{Mg}{4}$$ on the floor (by Newton's third law, the floor exerts the same force on the block).

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

$$g - a = \frac{g}{4}$$

$$a = g - \frac{g}{4} = \frac{3g}{4}$$

Hence, the correct answer is Option B: $$\dfrac{3g}{4}$$.