A liquid column of height 0.04 cm balances excess pressure of a soap bubble of certain radius. If density of liquid is 8 × 10³ kg m⁻³ and surface tension of soap is 0.28 N m⁻¹, then diameter of the soap bubble is __________ cm. (if g = 10 m s⁻²) Numerical answer type. Work it out, then open the answer.

Answer: 7. Soap bubble has two surfaces: Δ P = 4T/r, balanced by hρ g. hρ g = 4 × 10⁻⁴ × 8 × 10³ × 10 = 32 Pa r = (4T)/(hρ g) = (4 × 0.28)/(32) = 0.035 m = 3.5 cm Diameter = 2r = 7 cm

A liquid column of height 0.04 cm balances excess pressure of a soap… | JEE Main 2024 (8 Apr, Shift 1)

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Excess Pressure: Drops & Bubbles

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

Numerical answer type. Work it out, then open the answer.

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Answer: 7

Soap bubble has two surfaces: $\Delta P = \frac{4T}{r}$ , balanced by $h\rho g$ .
$h\rho g = 4 \times 10^{-4} \times 8 \times 10^3 \times 10 = 32\text{ Pa}$
$r = \frac{4T}{h\rho g} = \frac{4 \times 0.28}{32} = 0.035\text{ m} = 3.5\text{ cm}$
Diameter $= 2r = 7\text{ cm}$

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