A wooden block is floating in a liquid, 50% of its volume is inside the liquid when the vessel is stationary. Percentage of volume immersed when the vessel moves upwards with an acceleration $a=g/2$  is:

When the vessel is stationary:
Weight = upthrust
i.e.,    $V{\rho }_{w}g=V_i{\rho }_{L}g$             
(  density of wood and  ${\rho }_L=$ density of liquid)
Or     $\frac{V_i}{V}=\frac{{\rho }_w}{{\rho }_L}\mathrm{.............}\left(i\right)$                        
When the vessel moves upwards:
Upthrust – weight = (mass) (acceleration)
Or    $V{\text{'}}_i{\rho }_L(g+g/2)-V_{{\rho }_w}g=\frac{V{\rho }_{w}g}{2}$            
Or    $\frac{V{\text{'}}_i}{V}=\frac{{\rho }_w}{{\rho }_L}\mathrm{..........}\left(ii\right)$               
From Eqs. (i) and (ii), we see that
  $\frac{V_i}{V}=\frac{V\text{'}}{V}$
i.e., fraction (or percentage) or volume immersed in liquid remains unchanged.