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An air bubble at a depth of 20 cm in water has a radius of 1 mm. If the inner pressure of the bubble is greater than the…

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An air bubble at a depth of 20 cm in water has a radius of 1 mm. If the inner pressure of the bubble is greater than the atmospheric pressure by \(2100\mathrm{N}/{\mathrm{m}}^{2}\), find the surface tension of the bubble.

a

\(\text{0.025 }\text{N/m}\)

b

\(0.25\text{ }\text{N/m}\)

c

\(\text{0.5 }\text{N/m}\)

d

\(\text{0.05 }\text{N/m}\)

✓ Correct answer: d)

\(\text{0.05 }\text{N/m}\)

Explanation

Here, Pi - Po = 2100 ... (1)

Let the pressure at the depth is Po'.

\({\mathrm{P}}_{\mathrm{o}}^{'}={\mathrm{P}}_{\mathrm{o}}+\rho \mathrm{g}\mathrm{h}\\ \mathrm{So},\\ {\mathrm{P}}_{\mathrm{i}}-{\mathrm{P}}_{\mathrm{o}}^{'}=\frac{2\mathrm{T}}{\mathrm{R}}\\ {\mathrm{P}}_{\mathrm{i}}={\mathrm{P}}_{\mathrm{o}}+\rho \mathrm{g}\mathrm{h}+\frac{2\mathrm{T}}{\mathrm{R}}\\ {\mathrm{P}}_{\mathrm{o}}+2100={\mathrm{P}}_{\mathrm{o}}+1000\times 10\times 0.2+\frac{2\mathrm{T}}{{10}^{-3}}\)

\(100=\frac{2T}{R}\)

\(\Rightarrow T=\frac{100\times {10}^{-2}}{20}\)

= 0.05 N/m

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