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A small sphere falls from rest in a visc...

A small sphere falls from rest in a viscous liquid. Due to friction, heat is prodced. Find the relation between the rate of production of heat and the radius of the sphere at terminal velocity.

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Viscous force on a falling sphere in a liquid `F=pietav_(T)`
where `v_(T)=(2.9)r^(2)(rho-sigma)g.eta` is terminal velocity `rho=` density of sphere `sigma=`density of liquid
Rate of production of heat `=(="power")=Fv_(T)=6pietarv_(1)^(2)`
`=6pietar[2/9(r^(2)(rho-sigma)g)/eta]^(2)=8/27(pig^(2)(rho-sigma)^(2))/etar^(5)`
clearly
`(dQ)/(dt)propr^(5)`
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