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MHT CET20249 May 2024Evening ShiftPhysicsMechanical Properties of FluidsActual

The work done in splitting a water drop of radius R into 64 droplets is ( T = Surface tension of water)

Options

  1. A6 TR ^2
  2. B12 TR ^2
  3. C8 TR ^2
  4. D24 TR ^2

Correct answer

B. 12 TR ^2

Step-by-step solution

Given the radius of drop is R . Let r be the radius of smaller droplets. As the total volume remains the same, array ll & 4 3 R^3=64 4 3 r^3 & r= R (64)^ 1 3 = R 4 array Initial surface energy E₁=4 R^2 T Final surface energy E₂=64 4 ( R 4 )^2 T=16 R ^2 ~T Work done, W = E ₂- E ₁ W =12 TR ^2

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