JEE Main · 2020 · 03 Sep 2020 · Shift 1 · Fluid Mechanics

Pressure inside two soap bubbles are 1.01 and 1.02 atmosphere, respectively. The ratio of their volumes is

(A) $4 : 1$
(B) $0.8 : 1$
(C) $2 : 1$
(D) $8 : 1$ ✓ Correct

Answer: (D)

Solution

The pressure in excess of the atmosphere inside a soap bubble is

Δ P = \frac{4 T}{R}

, so the radius is inversely proportional to the excess pressure. The two bubbles have excess pressures

0.01

atm and

0.02

atm, giving

\frac{R _{1}}{R _{2}} = \frac{0.02}{0.01} = 2

. Volume grows as the cube of the radius, so

\frac{V _{1}}{V _{2}} = 2^{3} = 8

, a ratio of

8 : 1

JEE Main · 2020 · 03 Sep 2020 · Shift 1 · Single correct option

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