Question

Two block of wood of masses $m_1$and $m_2$ and each of specific gravity 0.5 are submerged at a depth of $h_1$ and $h_2$ in
a vessel $(h_2>h_1)$ filled with water, which is accelerated upwards with an acceleration $\frac{g}{2}$. the difference in
time taken by the blocks to reach the surface, when released with zero velocity is :

• A. zero
• B. $2\sqrt{\frac{(h_2-h_1)}{2g}}$
• C. $\sqrt{\frac{(h_2-h_1)}{g}}$
• D. $2\sqrt{\frac{(h_2-h_1)}{3g}}$

Answer 1

The correct option is D $2\sqrt{\frac{(h_2-h_1)}{3g}}$

Let $a_1$ and $a_2$ be the accelerations upwards of the two blocks
$a_1=\frac{upthrust-weight}{m_1}=\frac{1}{m_1}[\frac{m_1}{0.5\times {10}^3}\times {10}^3\times (g+\frac{4}{2})-m_{1}g]=2g$
Similiarly, $a^2=2g$
Accceleration fo blocks relative to water= $2g-\frac{g}{2}=3\frac{g}{2}$
$h_1=\frac{1}{2}\times \frac{3g}{2}{t}_1^2$
$t_1=2\sqrt{\frac{h_1}{3g}}$ and $t_2=2\sqrt{\frac{h_2}{3g}}$
$t_2-t_1=2\sqrt{\frac{(h_2-h_1)}{3g}}$