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Thermodynamics

Question
CBSEENPH11020841

A small sphere of radius 'r' falls from rest in a viscous liquid. As a result, heat is produced due to viscous force. The rate of production of heat when the sphere attains its terminal velocity, is proportional to

  • r3

  • r2

  • r4

  • r5

Solution

D.

r5

Power = rate of production of heat= F.V

 = 6πηrvτ.Vτ = 6πηrVτ2( F = 6πηVτr    stoke's formula)Vτ  r2 Vτ = 29r2(ρ -σ)ηg Power  r5