Question

The surface tension of soap solution at a temperature $20^{\circ }C$ is $2.5\times 10^{-2}N{m}^{-1}$. The excess pressure inside a bubble of soap solution of radius $6mm$ is, if an air bubble of the same dimensions were formed at a depth of $30cm$ inside a container containing the soap solution of relative density $1.20$, then the pressure inside the bubble is (Take $1atm=1.01\times 10^{5}Pa)$

• A. $1.01\times 10^{4}Pa$
• B. $1.05\times 10^{5}Pa$
• C. $2.01\times 10^{4}Pa$
• D. $3.01\times 10^{4}Pa$

Answer 1

Answer: (B)

Here, $h=30cm=30\times 10^{-2}m$
$P_0=1.01\times 10^{5}Pa$,
${\rho }_{soap}=1.2\times 10^{3}kg{m}^{-3}$
Excess pressure inside the air bubble,
$P^{\prime }=\frac{2S}{r}=\frac{2\times 2.5\times 10^{-2}}{6\times 10^{-3}}=8.3Pa$
Pressure inside the air bubble at depth $h$ in soap solution
$=P^{\prime }+P_0+h\rho g$
$=8.3+1.01\times 10^5+30\times 10^{-2}\times 1.2\times 10^3\times 9.8$
$=1.05\times 10^{5}Pa$