The excess pressure inside a spherical soap bubble of radius $1 \mathrm{~cm}$ is balanced by a column of oil…

The excess pressure inside a spherical soap bubble of radius $1 \mathrm{~cm}$ is balanced by a column of oil (Specific gravity $=0.8$ ), $2 \mathrm{~mm}$ high , the surface tension of the bubble is
  1. $3.92 \mathrm{~N} / \mathrm{m}$
  2. $0.0392 \mathrm{~N} / \mathrm{m}$
  3. $0.392 \mathrm{~N} / \mathrm{m}$
  4. $0.00392 \mathrm{~N} / \mathrm{m}$

Solution

The excess pressure of soap bubble $p=\frac{4 T}{R}$ $h \rho g=\frac{4 T}{R}$ $\therefore T=\frac{R h \rho g}{4}$ $=\frac{1 \times 10^{-2} \times 2 \times 10^{-3} \times 0.8 \times 10^3 \times 9.8}{4}$ $=3.92 \times 10^{-2} \mathrm{~N} / \mathrm{m}$ $=0.0392 \mathrm{~N} / \mathrm{m}$

Asked in: AP EAMCET 2010

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