A small sphere of radius r falls from rest in a viscous liquid. As a result, heat is produced due to viscous…

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 terminal velocity, is proportional to
  1. r5
  2. r2
  3. r3
  4. r4

Solution

Rate of heat produced = power of viscous force
terminal velocity V T = 2 r 2 ( ρ−σ )g 9η
⇒ V T ∝ r 2
dQ dt =6πηr  V T × V T
⇒ dQ dt ∝ r 5 .

Asked in: NEET 2018

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