Question

Find the ratio between the depths where the pressures are $3\times {10}^{5}N{m}^{-2}$ and $5\times {10}^{5}N{m}^{-2}.(P_A={10}^{5}N{m}^{-2})$

Answer 1

Let the pressure $P_1=3\times {10}^5=P_A+\rho gh$

Let the pressure $P_2=5\times {10}^5=P_A+\rho gH$

$h=\frac{P_1-P_A}{\rho g}$

Also $H=\frac{P_2-P_A}{\rho g}$

On dividing above equation,

$\frac{H}{h}=\frac{5\times {10}^5-{10}^5}{3\times {10}^5-{10}^5}$

$\frac{H}{h}=2$

$⟹\frac{h}{H}=1:2$