MHT CET202525 Apr 2025Evening ShiftPhysicsMechanical Properties of FluidsActual
The amount of work done in blowing a soap bubble such that its diameter increases from ' d ' to ' D ' is ( T = surface tension of solution)
Options
- A(D^2-d^2 ) T
- B2 (D^2-d^2 ) T
- C4 (D^2-d^2 ) T
- D8 (D^2-d^2 ) T
Correct answer
B. 2 (D^2-d^2 ) T
Step-by-step solution
Work Done in Soap Bubble Expansion The work done equals the surface tension multiplied by the change in total surface area. A soap bubble has two surfaces—inner and outer—each contributing to the area. The initial diameter is d and final diameter is D , so initial radius r₁ = d/2 and final radius r₂ = D/2 . The total initial surface area is A₁ = 2 4 r₁^2 = 8 (d/2)^2 = 2 d^2 . The total final surface area is A₂ = 2 4 r₂^2 = 8 (D/2)^2 = 2 D^2 . The change in surface area is A = A₂ - A₁ = 2 (D^2 - d^2) . Thus the work