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:

Difficult

A

r³
B

r²
C

r⁵
D

r⁴

Solution

Rate of heat produced
$\frac{dQ}{dt} = F_{v} \times v_{T} ∵ v_{T} = \frac{2 r^{2}}{9 η} (ρ - σ) g \infty r^{2} = 6 {πηrv}_{T} \times v_{T} \Rightarrow \frac{dQ}{dt} \infty {rv}_{T}^{2} \infty r^{5}$

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