First slide

Viscosity

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

Easy

A

r³
B

r²
C

r⁴
D

r⁵

Solution

Viscous drag F_D = 6πηrV_T Also V_T $\large \propto$ r²
Rate of production of heat (Q) = Power dissipated
= F_D.V_T
$\large \therefore$ Q = 6πηr(V_T)² ⇒ Q $\large \propto$ r x (r²)²

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