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Question: The work done in blowing a soap bubble of radius \(0.2m\), given that the surface tension of soap...

The work done in blowing a soap bubble of radius 0.2m0.2m, given that the surface
tension of soap solution is 60×10−3Nm−160 \times {10^{ - 3}}N{m^{ - 1}} is:
(A) 24π×10−2J24\pi \times {10^{ - 2}}J
(B) 4π×10−4J4\pi \times {10^{ - 4}}J
(C) 96π×10−4J96\pi \times {10^{ - 4}}J
(D) 1.92π×10−2J1.92\pi \times {10^{ - 2}}J

Explanation

Solution

In order to solve the question we need to know about surface tension Surface tension is the property of any liquid by virtue of which tries to minimize its free surface area. Surface tension of a liquid is measured as the force acting per length on an imaginary line drawn tangentially on the free surface of the liquid.
Surface tension
S = forcelength\dfrac{{force}}{{length}} = FL\dfrac{F}{L}=work donechange in area\dfrac{{work\,done}}{{change\,in\,area}}
Its SI unit is Nm−1N{m^{ - 1}} or Jm−2J{m^{ - 2}}
its dimensional formula is [MT−2]\left[ {M{T^{ - 2}}} \right]
Work Done in Blowing a Soap Bubble As a soap bubble has two free surfaces, hence work done in blowing a soap bubble so as to increase its radius from r1{r^1} to r2{r^2} is given by
W=8×π×S×R2W = 8 \times \pi \times S \times {R^2} ….eq(1)

Complete step by step solution:
Given
S=60×10−3Nm−1=0.060Nm−1S = 60 \times {10^{ - 3}}N{m^{ - 1}} = 0.060N{m^{ - 1}}
(R)=0.2m(R) = 0.2m
Put the value in equation 1
W=8×π×0.060×(0.2)2W = 8 \times \pi \times 0.060 \times {(0.2)^2}
W=0.0192πJW = 0.0192\pi J
W=1.92×10−2 JW = 1.92 \times {10^{ - 2}}\,J

So the correct option is D

Note:
Surface tension is a scalar quantity. Surface tension is a molecular phenomenon which is due to cohesive force and the root cause of the force is electrical in nature.
Surface tension of a liquid depends only on the nature of the liquid and independent of the surface area of film or length of the line .
Small liquid drops are spherical due to the property of surface tension.
Adhesive Force
The force of attraction acting between the molecules of different substances is called adhesive force, e.g., the force of attraction acting between the molecules of paper and ink, water and glass, etc.
Cohesive Force
The force of attraction acting between the molecules of the same substance is called cohesive force. e.g., the force of attraction acting between molecules of water, glass, etc.
Cohesive forces and adhesive forces are van der Waals’ forces.
These forces vary inversely as the seventh power of distance between the molecules.