Question

A small block of wood of specific gravity $0.5$ is submerged at a depth of $1.2m$ in a vessel filled with the water. The vessel is accelerated upwards with an acceleration $a_0=g/2$. Time taken by the block to reach the surface, if it is released with zero initial velocity is

• A. 0.6 s
• B. 0.4 s
• C. 1. 2 s
• D. 1 s

Answer 1

Answer: (B)

Let $m$ be the mass of block and $a$ its acceleration in upward direction. Then.

$a=\frac{\text{ upward thrust }-\text{ weight }}{m}=\frac{F-w}{m}$
$\Rightarrow a=\frac{\left(\frac{m}{0.5\times 10^3}\right)\times \left(10^3\right)\times \left(g+a_0\right)-mg}{m}$
$\Rightarrow a=2\left(g+\frac{g}{2}\right)-g=2g$
Acceleration of block relative to water
$a_r=a-a_0=2g-\frac{g}{2}=\frac{3g}{2}$
$\therefore h=\left(\frac{1}{2}\right)a_r{t}^2$
$\Rightarrow t=\sqrt{\frac{2h}{a_r}}=\sqrt{\frac{2h}{\frac{3}{2}g}}=2\sqrt{\frac{h}{3g}}=2\sqrt{\frac{1.2}{3\times 10}}m$
$\Rightarrow t=0.4s$