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 g/3, the fraction of volume immersed in the liquid will be 

Let x be the fraction of volume immersed when vessel is not accelerating, then

$\begin{array}{l}W=Upthrust\\ V{\rho }_{b}g=xV{\rho }_{l}g\\ x=\frac{{\rho }_b}{{\rho }_l}\end{array}$

When the vessel is accelerating upward let y be the fraction of volume immersed, then 

Net force = Upthrust – weight 

$\begin{array}{l}V{\rho }_b\frac{g}{3}=yV{\rho }_l\left(g+\frac{g}{3}\right)-V{\rho }_{b}g\\ y=\frac{{\rho }_b}{{\rho }_l}\end{array}$

From the above we can see , i.e., the fraction of volume immersed does not change by the acceleration of vessel.