A liquid column of height 0.04 cm balances excess pressure of soap bubble of certain radius. If density of liquid is $8 \times 10^{3} \mathrm{~kg} \mathrm{~m}^{-3}$ and surface tension of soap solution is $0.28 \mathrm{Nm}^{-1}$, then diameter of the soap bubble is \_\_\_\_ cm. (if $\mathrm{g}=10 \mathrm{~ms}^{-2}$)

JEE Main · 2024 · 08 Apr 2024 · Shift 1 · Fluid Mechanics

A liquid column of height 0.04 cm balances excess pressure of soap bubble of certain radius. If density of liquid is

8 \times 1 0^{3} kg m^{- 3}

and surface tension of soap solution is

0.28 Nm^{- 1}

, then diameter of the soap bubble is ____ cm.
(if

g = 10 ms^{- 2}

)

Answer: 7

Solution

The liquid column balances the excess pressure of the soap bubble (two surfaces):

ρ g h = \frac{4 S}{R}

, so

R = \frac{4 S}{ρ g h} = \frac{4 ( 0.28 )}{( 8 \times 1 0 ^{3} ) ( 10 ) ( 4 \times 1 0 ^{- 4} )} = \frac{1.12}{32} = 0.035 m = 3.5 cm

Diameter

= 2 R = 7 cm

JEE Main · 2024 · 08 Apr 2024 · Shift 1 · Integer answer

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