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Question: The work done in forming a soap film of size \(10cm \times 10cm\) will be, if the surface tension of...

The work done in forming a soap film of size 10cm×10cm10cm \times 10cm will be, if the surface tension of the soap solution is 3×10−2N/m3 \times {10^{ - 2}}N/m.
A) 3×10−4J3 \times {10^{ - 4}}J
B) 3×10−2J3 \times {10^{ - 2}}J
C) 6×10−4J6 \times {10^{ - 4}}J
D) 6×10−2J6 \times {10^{ - 2}}J

Explanation

Solution

To solve this problem one must be aware of the relationship between the energy and the work or the work-energy theorem etc. According to the work-energy theorem work and energy are mutually interconvertible. However, the exact statement of the work-energy theorem is that the net work done by the forces acting on an object is equal to its change in kinetic energy.

Complete step by step answer: It is given in the problem that the surface area of the film is , but we know that a soap film has two surfaces, hence, the surface area of the film is,
ΔA=2×10×10cm2⇒ΔA=2×10−2cm2\Delta A = 2 \times 10 \times 10c{m^2} \Rightarrow \Delta A = 2 \times {10^{ - 2}}c{m^2}
Also the surface tension in the problem is given to be, T=3×10−2N/mT = 3 \times {10^{ - 2}}N/m
Now we know that the energy required to form a soap film is given by the product of the surface tension and the surface area. This is mathematically given below in equation (1).
E=T×ΔAE = T \times \Delta A ……….. (1)
Putting the values of tension (T) and surface area of the film in equation (1), we get
E=3×10−2×2×10−2E = 3 \times {10^{ - 2}} \times 2 \times {10^{ - 2}}
⇒E=6×10−4J\Rightarrow E = 6 \times {10^{ - 4}}J ……. (2)
We know that energy and work are mutually interconvertible and under ideal conditions where there are no losses we can say that work done is equal to the energy.
W=EW = E ….. (3)
From equation (2) and equation (3) we have,
W=6×10−4JW = 6 \times {10^{ - 4}}J
We have found the work done in forming the given soap film to be 6×10−4J6 \times {10^{ - 4}}J.

Hence, we can say that option (C) is the correct answer option.

Note: Following key points regarding the surface tension must be kept in mind.
Surface tension is a property of fluids on account of which the fluids tend to minimise or shrink their surface area
Surface tension is the force acting per unit length of the surface of a fluid.
The unit of surface tension is N/m.