Under isothermal condition, two soap bubbles of radii r₁ and r₂… | MHT CET 2026 (16 Apr, Shift 2)

Q14MHT CET 2026 · 16 APR · SHIFT 2Difficult

Excess Pressure: Drops & Bubbles

Under isothermal condition, two soap bubbles of radii $r_1$ and $r_2$ combine to form a single soap bubble of radius R. The surface tension of the soap is (P = outside pressure)

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Answer: (a)

Isothermal: $P_{in}V$ total is conserved, with $P_{in} = P + \frac{4T}{r}$ .
$\left(P + \frac{4T}{R}\right)R^3 = \left(P + \frac{4T}{r_1}\right)r_1^3 + \left(P + \frac{4T}{r_2}\right)r_2^3$
$P(R^3 - r_1^3 - r_2^3) = 4T(r_1^2 + r_2^2 - R^2)$
$T = \frac{P(R^3 - r_1^3 - r_2^3)}{4(r_1^2 + r_2^2 - R^2)}$
So the answer is (a).

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Excess Pressure: Drops & Bubbles question from MHT CET 2026 (16 Apr, Shift 2)

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