Question

The temperature of an air bubble while rising from bottom to surface of a lake remains constant but its diameter is doubled. If the pressure on the surface is equal to h meter of mercury column and relative density of mercury is $\rho$, then the depth of the lake in meter, is

• A. $2\rho h$
• B. $4\rho h$
• C. $8\rho h$
• D. $7\rho h$

Answer 1

The correct option is D $7\rho h$

$p_1{V}_1=p_2{V}_2$

$(H{\rho }_{w}g+h{\rho }_{Hg}g)\frac{4}{3}\pi r^3=\left(h{\rho }_{Hg}g\right)\left(\frac{4}{3}\pi {\left(2r\right)}^3\right)$

$\Rightarrow H{\rho }_{\omega }=7\rho {}_{Hg}$

$\therefore H=\frac{7h{\rho }_{hg}}{{\rho }_{\omega }}=7h\rho$