Question

A wooden block is floating in a liquid $50\%$ of its volume inside the liquid when the vessel is stationary. Percentage of volume immersed when the vessel moves upwards with an acceleration $a=g/3$ is

• A. $30\%$
• B. $50\%$
• C. $60\%$
• D. $67\%$

Answer 1

Answer: (B)

Let densities of wood and liquid are ${\rho }_w$ and ${\rho }_l$ respectively.
When vessel is stationary weight $=$ upthrust
ie, $V{\rho }_{w}g=V_l{\rho }_{l}g$
or $\frac{V_l}{V}=\frac{{\rho }_w}{{\rho }_l}\dots .(i)$
When the vessel moves upwards with acceleration $g/3.$
upthrust - weight $=$ mass $\times$ acceleration
$V_l{\rho }_l\left(g+\frac{g}{3}\right)-V{\rho }_{w}g=V{\rho }_w\times \frac{g}{3}$
$\frac{V_1}{V}=\frac{{\rho }_w}{{\rho }_l}\dots ..$ (ii)
From Eqs. (i) and (ii), we note that
$\frac{V_l}{V}=\frac{V_l}{V}$
ie, fraction of volume immersed in liquid remains unchanged.