Question
A soap bubble of radius $$R$$ is surrounded by another soap bubble of radius $$2R,$$ as shown. Take surface tension $$= S.$$ Then the pressure inside the smaller soap bubble, in excess of the atmospheric pressure, will be
A soap bubble of radius $$R$$ is surrounded by another soap bubble of radius $$2R,$$ as shown. Take surface tension $$= S.$$ Then the pressure inside the smaller soap bubble, in excess of the atmospheric pressure, will be
A.
$$\frac{{4S}}{R}$$
B.
$$\frac{{3S}}{R}$$
C.
$$\frac{{6S}}{R}$$
D.
None of these
Answer :
$$\frac{{6S}}{R}$$
Solution :
$$\eqalign{ & {P_1} - {P_0} = \frac{{4S}}{{2R}}\,......\left( {\text{i}} \right) \cr & {P_2} - {P_1} = \frac{{4S}}{R}\,......\left( {{\text{ii}}} \right) \cr} $$
Add (i) and (ii),
$${P_2} - {P_0} = \frac{{6S}}{R}$$
$$\eqalign{ & {P_1} - {P_0} = \frac{{4S}}{{2R}}\,......\left( {\text{i}} \right) \cr & {P_2} - {P_1} = \frac{{4S}}{R}\,......\left( {{\text{ii}}} \right) \cr} $$
Add (i) and (ii),
$${P_2} - {P_0} = \frac{{6S}}{R}$$
