Question

At room temperature, two bubbles of radii 8 cm and 15 cm are connected by a capillary tube. The final radii of the two bubbles respectively are (Neglect the volume of the air in the capillary tube)

• A. 0 cm, 15.72 cm
• B. 11.5 cm, 11.5 cm
• C. 0 cm, 17 cm
• D. 12.5 cm, 12.5 cm

Hint:

When bubbles are connected, the smaller bubble shrinks, larger grows until pressures equal.

Answer 1

The Correct Option is B

1. Pressure inside a bubble: $P = P_0 + \frac{2T}{R}$, $T$ = surface tension.
2. Air flows from smaller bubble (higher pressure) to larger bubble (lower pressure) until pressures equal.
3. Total volume: $V_\text{total} = \frac{4}{3}\pi (8^3 + 15^3) \approx 13909~\text{cm}^3$
4. Equal radii after equilibrium: $2 \cdot \frac{4}{3}\pi R_f^3 = V_\text{total} \implies R_f \approx 11.5~\text{cm}$