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  • Find the depth at which an air bubble of radius will remain in equilibrium in water.

Find the depth at which an air bubble of radius 0.7 \mathrm{~mm} will remain in equilibrium in water. Given, surface tension of water \mathrm{=7.0 \times 10^{-2} \mathrm{Nm}^{-1}}. Take \mathrm{g=10 \mathrm{~ms}^{-2}.}

Option: 1

2 cm


Option: 2

3 cm


Option: 3

4 cm


Option: 4

5 cm


Answers (1)

best_answer

The bubble will be in equilibrium at a depth h if excess pressure \mathrm{\frac{2 \sigma}{r}=h \rho g} or \mathrm{h=\frac{2 \sigma}{r \sigma g}.} Given \mathrm{\sigma =7.0 \times 10^{-2} \mathrm{Nm}^{-1}, r=0.7 \times 10^{-3} \mathrm{~m}, \rho=10^3 \mathrm{~kg} \mathrm{~m}^{-3}} and \mathrm{g=10 \mathrm{~ms}^{-2}.} Using these values, we get \mathrm{h=4 \times 10^{-2} \mathrm{~m}=4 \mathrm{~cm}}, which is choice (c).

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rishi.raj

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