Question

A bubble is at the bottom of the lake of depth $h$ . As the bubble comes to surface, its radius increases three times. If atmospheric pressure is equal to $l \, $ metre of water column, then $h$ is equal to

• A. $26 \, l$
• B. $l$
• C. $25 \, l$
• D. $30 \, l$

Answer 1

Answer: (A)

From Boyle's law
$pV=$ constant
$\therefore \, \, p_{1}V_{1}=p_{2}V_{2}$
Here, $p_{1}=\rho g\left(h + l\right), \, \, V_{1}=\frac{4}{3}\pi r^{3}$
$p_{2}=\rho g l, \quad V_{2}=\frac{4}{3} \pi(3 r)^{3}$
$\therefore \, \left(h + l\right)\frac{4}{3}\pi r^{3}=l\times \frac{4}{3}\pi \left(3 r\right)^{3}$
or $ \, \, \, h+l=27l$
$\therefore \, h=26l$