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 $\frac{V_{l}}{V}=\frac{\rho_{w}}{\rho_{l}} \ldots .( i )$
When the vessel moves upwards with acceleration $g / 3 .$
upthrust - weight $=$ mass $\times$ acceleration
$V_{l} \rho_{l}\left(g+\frac{g}{3}\right)-V \rho_{w} g=V \rho_{w} \times \frac{g}{3}$
$\frac{V_{1}}{V}=\frac{\rho_{w}}{\rho_{l}} \ldots . .$ (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.