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MHT CET202526 Apr 2025Evening ShiftPhysicsMechanical Properties of FluidsActual

Under isothermal conditions, two soap bubbles of radii r₁ and r₂ coalesce to form a big drop. The radius of the big drop is

Options

  1. A(r₁+r₂ )^ 1 2
  2. B(r₁+r₂ )^2
  3. C(r₁^2+r₂^2 )^ 1 2
  4. D(r₁+r₂ )^3

Correct answer

C. (r₁^2+r₂^2 )^ 1 2

Step-by-step solution

The radius R of a large soap bubble formed from the coalescence of two bubbles with radii r₁ and r₂ under isothermal conditions can be determined by conserving the total number of moles of gas. Given that PV = nRT and assuming isothermal conditions, the conservation equation becomes P_f V_f = P₁ V₁ + P₂ V₂ . For soap bubbles, the internal pressure is P = P_ atm + 4T r , and the volume is V = 4 3 r^3 . Substituting yields: (P_ atm + 4T R ) 4 3 R^3 = (P_ atm + 4T r₁ ) 4 3 r₁^3 + (P_ atm + 4T r₂ ) 4 3 r₂^3 . Assuming

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