Fluid Mechanics

JEE Main level, numerical answer, medium

105 of 192

Question 105 of 192

A liquid column of height 0.04 cm0.04 \mathrm{~cm} balances excess pressure of a soap bubble of certain radius. If density of liquid is 8×103 kg m−38 \times 10^3 \mathrm{~kg} \mathrm{~m}^{-3} and surface tension of soap solution is 0.28Nm−10.28 \mathrm{Nm}^{-1}, then diameter of the soap bubble is _____ cm\mathrm{cm}. (if g=10 m s−2g=10 \mathrm{~m} \mathrm{~s}^{-2} )

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Answer: 7

ρgh=4 SR⇒R=4×0.288×103×10×4×10−4⇒0.288 m=288 cm⇒R=3.5 cm\begin{aligned} & \rho \mathrm{gh}=\frac{4 \mathrm{~S}}{\mathrm{R}} \\ & \Rightarrow \mathrm{R}=\frac{4 \times 0.28}{8 \times 10^3 \times 10 \times 4 \times 10^{-4}} \\ & \Rightarrow \frac{0.28}{8} \mathrm{~m}=\frac{28}{8} \mathrm{~cm} \\ & \Rightarrow \mathrm{R}=3.5 \mathrm{~cm}\end{aligned}
Diameter =7 cm=7 \mathrm{~cm}

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