A small spherical ball falling under gravity in a viscous medium heat the medium due to viscous drag force. The rate of heating is proportional to rn. Find the value of n. [r=radius of sphere]
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Solution
Let the terminal velocity be ‘v’ then rate of heating is ddt(PE) ⇒ddt(mgvt)=mgv ∴v=2r29η(σ−ρ)g ∴ΔPEΔt=43πr3σg⋅2r29η(σ−ρ)g ∴ Rate of heating ∝r5