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Q.

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

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a

r4

b

r3

c

r5

d

r2

answer is C.

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Detailed Solution

Rate of heat produced = power loss against viscous force⇒dQdt = Fv×vTwhere the terminal velocity, vT = 2r29η(ρ-σ)gand viscous force Fv = 6πηrvThence dQdt = 6πηrvT ×vT ⇒dQdt∝rvT2   but vT ∝ r2Hence dQdt∝r5
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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