Question

A soap bubble is formed from $10^{-3}g$ of soap solution. When it is filled with hydrogen of density $0.00009g/c{m}^3,$ it floats in impure argon gas of density $0.00199g/c{m}^3.$ What will be the excess pressure nearly in dyne per $c{m}^2$ ,If surface tension of soap solution is $12dyne/cm$ . (Take ${\pi }^{-1}=0.318$

Answer 1

Answer: 96

Let the volume of bubble be $V$ .
Balancing the weight, we get
$10^{-3}+0.00009V=0.00199V\Rightarrow V=\frac{10^{-3}}{1.9\times 10^{-3}}=0.526c{m}^3$
Since, $V=0.526=\frac{4}{3}\pi r^3\Rightarrow r=0.5cm$ .
Now, excess pressure, $P=\frac{4T}{r}=\frac{4\times 12}{0.5}=96dyneperc{m}^2$ .