Question

A cubical block is floating in a liquid with one fourth of its volume immersed in the liquid. If the whole of the system accelerates upwards with acceleration $g/4$, the fraction of volume immersed in the liquid will be

• A. $\frac{1}{4}$
• B. $\frac{1}{2}$
• C. $\frac{3}{4}$
• D. $\frac{2}{3}$

Answer 1

The correct option is A $\frac{1}{4}$

Upward acceleration will cause the effective acceleration due to gravity to increase due to downward pseudo force on the block. i.e $g_{eff}=g^{\prime }=(g+a)$

Condition for floating of body:
$F_b=mg$
$V_f{\rho }_{f}g=V_b{\rho }_{b}g...\left(i\right)$
where, $V_f\to$ volume of fluid displaced
and $V_f=\text{volume of immersed portion of cube}$

In case of system accelerating upwards, replacing $g\to g^{\prime }$ in Eq.$\left(i\right)$ will cancel out term $g^{\prime }$ from both sides.
$\Rightarrow V_f{\rho }_f=V_b{\rho }_b$
Hence it will not have any effect on the immersed volume of cube. $\frac{1}{4}th$ part will be the immersed portion.