Find the excess pressure inside (a) a drop of mercury of radius 2 mm (b) a soap bubble of radius 4 mm and (c) an air bubble of radius 4 mm formed inside a tank of water. Surface tension of mercury , soap solution and water are $0.46 N m^{- 1}, 0.03 N m^{- 1}$ and $0.076 N m^{- 1}$ respectively.

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Solution

r = 2 mm

$= 2 \times 10^{- 3} m,$

$T_{H g} = 0.465 N / m$

$T_{8} = 0.03 N / m$ ,

$T_{a} = 0.076 N / m$

P = $\frac{2 T_{H g}}{r}$

$= \frac{0.465 \times 2}{2 \times 10^{- 3}} = 465 N / m^{2}$

P = $\frac{4 T_{8}}{r}$

= $\frac{4 \times 0.03}{4 \times 10^{- 3}} = 30 N / m^{2}$

P = $\frac{2 T_{a}}{r}$

= $\frac{2 \times 0.076}{4 \times 10^{- 8}} = 38 N / m^{2}$

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Find the excess pressure inside (a) a drop of mercury of radius 2 mm (b) a soap bubble of radius 4 mm and (c) an air bubble of radius 4 mm formed inside a tank of water. Surface tension of mercury , soap solution and water are 0.46Nm−1,0.03Nm−1 and 0.076Nm−1 respectively.

r = 2 mm =2×10−3m, THg=0.465N/m T8=0.03N/m, Ta=0.076N/m P = 2THgr =0.465×22×10−3=465N/m2 P = 4T8r = 4×0.034×10−3=30N/m2 P = 2Tar = 2×0.0764×10−8=38N/m2

Find the excess pressure inside (a) a drop of mercury of radius 2 mm (b) a soap bubble of radius 4 mm and (c) an air bubble of radius 4 mm formed inside a tank of water. Surface tension of mercury , soap solution and water are $0.46 N m^{- 1}, 0.03 N m^{- 1}$ and $0.076 N m^{- 1}$ respectively.