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

Question

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, r 5, r 2, r 3, r 4

MARKS App · Accepted Answer

Rate of heat produced = power of viscous force terminal velocity V T = 2 r 2 ( ρ − σ ) g 9 η ⇒ V T ∝ r 2 d Q d t = 6 πη r V T × V T ⇒ d Q d t ∝ r 5

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