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A liquid has surface tension σ. The minimum work required to divide a spherical drop of this liquid of radius t into 8 equal-sized spherical drops is
  • a)
    πt2σ
  • b)
    2πt2σ
  • c)
    4πt2σ
  • d)
    8πt2σ
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A liquid has surface tension σ. The minimum work required to divide a...
The surface tension of a liquid is measured as the force acting per unit length on an imaginary line drawn tangentially on the free surface of the liquid.
Surface tension, S = Force/Length = F/L = Work done/Change in area
Work done in splitting a bigger drop (R) in ‘n’ smaller drops (r):
R3 = nr3 ⇒ r = n-1/3R
Here r = (8)-1/3t = 0.5 t
WD = 4πσ (nr2 – R2) = 4πσ (n(n-1/3R)2 – R2) = 4πσR2 (n1/3 – 1)
WD = 4πσt2 (81/3 – 1) = 4πσt2
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A liquid has surface tension σ. The minimum work required to divide a spherical drop of this liquid of radius t into 8 equal-sized spherical drops isa)πt2σb)2πt2σc)4πt2σd)8πt2σCorrect answer is option 'C'. Can you explain this answer?
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