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Q.

A small sphere falls from rest in a viscous liquid. Due to friction, heat is produced. Rate of production of heat at terminal velocity is related to radius r of the sphere as proportional to $r^{x}$ ,. Then $x =$

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a

2

b

3

c

4

d

5

answer is D.

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Detailed Solution

Rate of production of heat $= P = F v = 6 π η r v^{2}$
But, $v \propto r^{2} \Rightarrow P \propto r^{5}$

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