1. Identify the forces on the block

The block of mass $M$ is inside a box descending vertically with acceleration $a$.

For the block, the forces are:

• Weight downward: $Mg$
• Normal reaction by the floor upward: $N$

Given: the block exerts a force equal to one-fourth of its weight on the floor.

By Newton's third law, the floor exerts the same magnitude force on the block upward. So, $N = \frac{Mg}{4}$

2. Apply Newton's second law to the block

Since the box and block descend together, the block also has downward acceleration $a$.

Taking downward as positive: $Mg - N = Ma$

Substitute $N = \frac{Mg}{4}$: $Mg - \frac{Mg}{4} = Ma$

$\frac{3Mg}{4} = Ma$

Cancel $M$: $a = \frac{3g}{4}$

3. Match with the options

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

So the correct option is:

• C: $\frac{3g}{4}$

4. Compare with stored correct answer

Stored correct answer: C

This matches our derived answer.