Q 11-09-071JEE MainJEE Main 2024 (8 Apr, Shift 1)Easy
A liquid column of height $0.04\ \text{cm}$ balances the excess pressure of a soap bubble of certain radius. If the density of the liquid is $8\times10^3\ \text{kg m}^{-3}$ and the surface tension of the soap solution is $0.28\ \text{N m}^{-1}$, then the diameter of the soap bubble is ______ cm. (if $g = 10\ \text{m s}^{-2}$)
Numerical value type. Enter your answer.
Answer: 7
A soap bubble has two surfaces, so the excess pressure is $\dfrac{4T}{r}$:
$$\frac{4T}{r} = \rho gh \;\Rightarrow\; r = \frac{4\times0.28}{8\times10^3\times10\times4\times10^{-4}} = \frac{1.12}{32} = 0.035\ \text{m}$$
Diameter $= 7\ \text{cm}$.
Solution by Sreeraj P, M.Sc Physics