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Question

A soap bubble, having radius 1 mm, is blown from a detergent solution having a surface tension of 2.5×102 N/m. The pressure inside the bubble equals at a point Zo below the free surface of water in a container. Taking g=10 m/s2, density of water =103 kg/m3, the value of Z0 is
[Take g=10 m/s2]

A
5 cm
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B
8 cm
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C
1 cm
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D
3 cm
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Solution

The correct option is C 1 cm
Given,
Radius of soap bubble, R=1 mm=103 m
Surface Tension, T=2.5×102 N/m
Value of g=10 m/s2
Density of water, ρ=1000 kg/m3
Depth of water at which pressure is equal to pressure inside bubble =Zo= ?
Let us suppose, atmospheric pressure is po.
We know pressure inside soap bubble is given by
p=po+4TR
=po+4×2.5×102103
=po+100 ...........(1)
Pressure at depth Zo below free surface of water
p=p0+ρgZ0
=p0+1000×10×Zo
=p0+104Zo ...........(2)
Given, pressure at depth Zo is equal to pressure inside soap bubble.
From (1) and (2),
po+100=p0+104Zo
or Zo=102 m=1 cm

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