Question

A small block of wood of specific gravity $0.5$ is submerged at a depth of $1.2\text{m}$ in a vessel filled with water. The vessel is accelerated upwards with an acceleration $a_0=\frac{g}{2}$. Time taken by the block to reach the surface, if it is released with zero initial velocity is $\frac{x}{10}s$. Then find the value of $x$ :

Answer 1

$a=\frac{({\rho }_L-\rho ).V.g_{eff}}{\rho .V.}$
$a=(\frac{{\rho }_L}{\rho }-1)g_{eff}$
$a=(2-1)g_{eff}$
$a=g_{eff}=g+\frac{g}{2}$
$a=\frac{3g}{2}$
time = $\sqrt{\frac{2s}{a}}$
$=\sqrt{\frac{2\times 1.2\times 2}{3g}}=\sqrt{\frac{4\times 1.2}{3\times 10}}$
time $=0.4\text{sec}$