MHT CET · Physics · Mechanical Properties of Fluids
The surface tension of a soap solution is ' \(\mathrm{T}\) '. Work done in blowing a soap bubble of diameter \(2 \mathrm{~d}\) is
- A \(8 \pi d^2 T\)
- B \(2 \pi d^2 T\)
- C \(4 \pi d^2 T\)
- D \(6 \pi d^2 T\)
Answer & Solution
Correct Answer
(A) \(8 \pi d^2 T\)
Step-by-step Solution
Detailed explanation
In this case, work done = increase in surface energy, i.e.
\(\mathrm{W}=\mathrm{T} \Delta \mathrm{A}\)
Key point: In calculation, area of sphere have been multiplied with 2, since there are two surfaces in soap bubble.
\(\begin{aligned} & \therefore \mathrm{W}=\mathrm{T} \times\left[2\left(4 \pi \mathrm{d}^2\right)\right] \\ & \Rightarrow \mathrm{W}=8 \pi \mathrm{d}^2 \mathrm{~T}\end{aligned}\)
\(\mathrm{W}=\mathrm{T} \Delta \mathrm{A}\)
Key point: In calculation, area of sphere have been multiplied with 2, since there are two surfaces in soap bubble.
\(\begin{aligned} & \therefore \mathrm{W}=\mathrm{T} \times\left[2\left(4 \pi \mathrm{d}^2\right)\right] \\ & \Rightarrow \mathrm{W}=8 \pi \mathrm{d}^2 \mathrm{~T}\end{aligned}\)
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