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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

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a
r3
b
r2
c
r5
d
r4
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detailed solution

Correct option is C

The viscous drag force, F=6πηrvwhere v= terminal velocity∴The rate of production of heat = power                                                                     = force ×times terminal velocity⇒ Power =6πηrv·v=6πηrv2∵ Terminal velocity v=2r2(ρ-σ)g9η;∴  v∝r2 Now, power =6πηr4r4(ρ-σ)281η2g2 or    Power ∝r5 .

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The terminal velocity of a small sized spherical body of radius r falling vertically in a viscous liquid is given by the following proportionality :

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