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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

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$R = r_{1} + r_{2}$

$R = \sqrt{r_{1}^{2} + r_{2}^{2}}$

$R = {(r_{1} + r_{2})}^{\frac{1}{2}}$

$R = [(r_{1} r_{2} (r_{1} + r_{2}))]$

answer is C.

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Detailed Solution

$2 \times 4 {πR}^{2} σ = 2 \times 4 {πr}^{2}_{1} σ + 2 \times 4 {πr}_{2}^{2} σ$

or $R^{2} = r_{1}^{2} + r_{2}^{2} or R = \sqrt{r_{1}^{2} + r_{2}^{2}}$

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