A soap bubble , having radius of 1 mm is blown from, a detergent solution having a surface tension , of 2.5 \times 10 ^{-2 } N/m. The pressure inside the bubble equals at a point Z_0 below  the free surface of water in a container of water = 10 ^ 3 Kg / m ^ 3 , the value of Z_0 is 

  • Option 1)

    100 cm 

  • Option 2)

    10 cm 

  • Option 3)

    1 cm 

  • Option 4)

    0.5 cm 

Answers (2)

r = 10 ^ {-3} \\\\ T = 2.5 \times 10 ^ {-2 } N/m \\\\ \Delta P = \frac{4 T}{r}

P_{z_0} = P_A + \rho g z_0 \\\\P_{z_0} - P_A = \delta g z_0 = 4 T / \gamma \\\\ Z_0 = \frac{4 T}{r } \times (1/ \rho y) \\\\ = \frac{4 \times 2.5 \times 10 ^{-2 }\times 1}{10 ^{-3}\times 10 ^ 3 \times 10 } \\\\ z_0 = 10 ^{-2} \\\\ z_0 = 1 cm


Option 1)

100 cm 

Option 2)

10 cm 

Option 3)

1 cm 

Option 4)

0.5 cm 

GIVEN : surface tension = force /length = 0.025 N/m

radius = 1mm = 0.001m

p(final) - p(initial) = 4t/r

where z is a pressure inside the bubble 

p(z=final) - p(initial) =pgh =pgz = 4t/r

pgz = 4t/r

z = 4t/pgr

z = 4(0.025)/(0.001)(1000)(10)

z =0.100/10

z = 0.100(0.1)

z = 0.01

z= 1(0.01)

z=1cm

option 3) 1cm

 

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