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MHT CET202522 Apr 2025Evening ShiftPhysicsMechanical Properties of FluidsActual

The excess pressure inside a soap bubble is 1.5 times the excess pressure inside a second soap bubble. The volume of the second bubble is ' x ' times the volume of the first bubble. The value of ' x ' is

Options

  1. A3 2
  2. B9 4
  3. C8 27
  4. D27 8

Correct answer

D. 27 8

Step-by-step solution

The excess pressure difference between soap bubbles follows P = 4T R , where T is surface tension and R the radius. Given P₁ = 3 2 P₂ , substituting the pressure formula yields: 4T R₁ = 3 2 4T R₂ Canceling 4T and rearranging gives R₂ R₁ = 3 2 . Since volume scales as R^3 , the volume ratio is: x = ( R₂ R₁ )^3 = ( 3 2 )^3 = 27 8 . The correct choice is D .

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