Question

Two spherical soap bubbles of radii $r_1$ and $r_2$ in vacuum coalesce under isothermal condition. The resulting bubble has a radius $R$ such that

• A. $R=\left[\right(r_1{r}_2(r_1+r_2)]$
• B. $R=(r_1+r_2{)}^{1/2}$
• C. $R=r_1+r_2$
• D. $R=\sqrt{r_1^2+r_2^2}$

Answer 1

The correct option is D $R=\sqrt{r_1^2+r_2^2}$

As given in question, two spherical soap bubbles of radii $r_1$ and $r_2$ in vacuum
As, Surface energy, $W=4\pi R^{2}T$
Now as process of combining is isothermal,
therefore,

$2\times 4\pi R^{2}T=2\times 4\pi r_1^{2}T+2\times 4\pi r_2^{2}T$

(As two soap bubbles)
Hence,

$R^2=r_1^2+r_2^2$

$R=\sqrt{r_1^2+r_2^2}$

Final answer: (c)