Question

The excess pressure in a soap bubble is double that in other one. The ratio of their volume is

• A. $1:2$
• B. $1:8$
• C. $1:4$
• D. $1:1$

Answer 1

Answer: (B)

Excess pressure in soap bubble $=\frac{4S}{R}$
Let for first bubble,
$P=\frac{4S}{R}$
$S-$ Surface tension
$R$ - Radius
For second bubble,
$2P=\frac{4S}{x}$
$S-$ Surface tension
$x-$ Radius
Substitute value of $P$
$2\times \frac{4S}{R}=\frac{4S}{X}$
$\Rightarrow x=\frac{R}{2}$
Ratio of Radii $=\frac{R/2}{R}=\frac{1}{2}$
So, Ratio of volume $=$ (Ratio of Radii) ${}^3$.
$={\left(\frac{1}{2}\right)}^3=\frac{1}{8}$