A cubical block is floating in a liquid with half of its volume immersed in the liquid. When the whole system accelerates upwards with acceleration of $\frac{\mathrm{g}}{3}$, the fraction of volume immersed in the liquid will be

Fraction of volume immersed in the liquid ${\mathrm{V}}_{\mathrm{in}} = \left(\frac{\mathrm{\rho }}{\mathrm{\sigma }}\right)\mathrm{V}$ i.e., it depends upon the densities of the block and liquid.
So there will be no change in it if system moves upward or downward with constant velocity or some acceleration.