Question

When an air bubble rises from the bottom to the surface of a lake, its radius becomes double. Find the depth of the lake. Given that the atmospheric pressure is equal to the pressure due toa column of water $10m$ high. Assume constant temperature and disregard surface tension

• A. $30m$
• B. $40m$
• C. $70m$
• D. $80m$

Answer 1

The correct option is C $70m$

$\text{Acc. to Boyles law}$

$P_1{v}_1=P_2{v}_2$

$(P_0+\rho gh)\frac{4}{3}\pi r^3=\left(P_0\right)\frac{4}{3}\pi (2r{)}^3$

$P_0\left(7r^3\right)=\rho gh{r}^3$

$(\rho g\times 10)7r^3={\rho ghr}^3$

$h=70m$

$\text{Answer:}\left(C\right)$