A block of mass m is kept on a platform which starts from rest with constant acceleration g/2 upward, as shown in fig. Work done bv normal reaction on block in time t is

Since the acceleration is upward-direction, the block will experience a pseudo-force that is represented by:

$F_p=m\times \frac{g}{2}$

Applying force balance to the block right now

$$\begin{gathered} N-mg=\frac{mg}{2} \\ N=\frac{3mg}{2} \end{gathered}$$

We know that a body travelling under gravity has the following displacement:

$S=ut+\frac{1}{2}g{t}^2$

The initial velocity is zero,

$$\begin{gathered} Work done, \\ W=NS \end{gathered}$$

$W=\left(\frac{3mg}{2}\right)\left(\frac{1}{2}g{t}^2\right)$

$W=\frac{3m{g}^2{t}^2}{4}$

Hence the correct answer is $\frac{3m{g}^2{t}^2}{4}.$