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

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Infinity Learn · Accepted Answer

The viscous drag force, $$F=6$$πηrvwhere $$v=$$ terminal velocity∴The rate of production of heat $$=$$ power                                                                     $$=$$ force ×times terminal velocity⇒ Power $$=6$$πηrv·$$v=6$$πη$$rv2$$∵ Terminal velocity $$v=2r2($$ρ$$-$$σ$$)g9$$η;∴  v∝$$r2$$ Now, power $$=6$$πη$$r4r4($$ρ$$-$$σ$$)281$$η$$2g2$$ or    Power ∝$$r5$$ .

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

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