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Question

# A small spherical drop fall from rest in viscous liquid. Due to friction, heat is produced. The correct relation between the rate of production of heat and the radius of the spherical drop at terminal velocity will be

A
dHdt1r5
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B
dHdtr4
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C
dHdt1r4
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D
dHdtr5
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Solution

## The correct option is C dHdt∝r5Viscous force acting on spherical dropFv=6πηv∴ Terminal velocity, v=29r2(σ−ρ)gηwhere, η= coefficient of viscosity of liquid σ= density of material of spherical drop ρ= density of liquidPower imparted by viscous force = Rate of production of heatρ=dHdt=Fv⋅v=6πηv2 =6πη⋅(29r2(σ−ρ)gη)2⇒dHdt∝r5

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