Question

A spherical soap bubble of radius 1 cm is formed inside another bubble of radius 3 cm The radius of a single soap bubble which maintains the same pressure difference as inside the smaller and outside the larger soap bubble is

• A. 0.75 cm
• B. 0.75 m
• C. 7.5 cm
• D. 7.5 m

Answer 1

Answer: (A)

Pressure outside the bigger drop $=P_1$
Pressure inside the bigger drop $=P_2$
Radius of bigger drop, $r_1=3cm$
Excess pressure $=P_2-P_1=\frac{4S}{r_1}=\frac{4S}{3}$
Pressure inside the smaller drop $=P_3$
Excess pressure $=P_3-P_2=\frac{4S}{r_2}=\frac{4S}{1}$
Pressure difference between inner side of smaller drop and outer side of bigger drop
$=P_3-P_1=P_3-P_2+P_2-P_1=\frac{4S}{1}+\frac{4S}{3}=\frac{16S}{3}$
This pressure difference should exist in a single drop of radius $r$.
$\therefore \frac{4S}{r}=\frac{16S}{3}$
or $r=\frac{3}{4}cm$
$=0.75cm$