Question

Two soap bubbles having radii $3cm$ and $4cm$ in vacuum, coalesce under isothermal conditions. The radius of the new bubble is

• A. $1cm$
• B. $5cm$
• C. $7cm$
• D. $3.5cm$

Answer 1

The correct option is B $5cm$

$\text{Given:-}$ Radius of soap bubble, $a=3cm$

Radius of soap bubble, $b=4cm$

$\text{Solution:-}$

Here,

$(p_0+\frac{4T}{a})\times \frac{4}{3}\pi a^3+(p_0+\frac{4T}{b})\times \frac{4}{3}\pi b^3$

$=(p_0+\frac{4T}{c})\times \frac{4}{3}\pi c^3$

$p_0(a^3+b^3)+4T(a^2+b^2)=p_0{c}^3+4T{c}^2$

Now, in vaccum, $p_0=0$

$\Rightarrow c=\sqrt{a^2+b^2}$

$=\sqrt{3^2+4^2}=5cm$

$\text{Hence the correct option is B}$