Q 11-09-023NEETJEE MainHard
Two soap bubbles of radii $3$ cm and $4$ cm join isothermally in vacuum to form a single bubble. The radius of the new bubble is
Answer: (A) $5$ cm
Concept. In vacuum the pressure inside is $\dfrac{4T}{r}$; isothermally $pV$ (amount of gas) is conserved.
Step 1. Conservation.
$$\frac{4T}{R}R^3 = \frac{4T}{r_1}r_1^3 + \frac{4T}{r_2}r_2^3 \;\Rightarrow\; R^2 = r_1^2 + r_2^2$$
Step 2. Solve. $R^2 = 9 + 16 = 25 \Rightarrow R = 5$ cm.
Answer. $5$ cm (Option A).
Solution by Sreeraj P, M.Sc Physics