NEET | 2018Fluid MechanicsEasy

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 its terminal velocity, is proportional to :-

Options

A.

r3

B.

r2

C.

r5

D.

r4

Solution

Rate of heat produced
dQdt=FV×VT     ∵ VT=2r29η(p-σ)g
= 6πηrVT × VT  ∴ VT  α  r2
dQdt∝ rVT2      ∵  VT ∝ r2
dQdt∝ r5

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