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 pr…

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 [NEET 2018]

Accepted Answer

Correct answer: D. (d) Rate of heat produced, dQ dt=F v_T Where, F is the viscous force and v_T is the terminal velocity. As, F=6 rv_T ⇒ dQ dt=6 rv_T v_T=6 rv_T^2 …(i) From the relation for terminal velocity, v_T= 29 r^2 ( - ) g we get v_T ∝r^2 …(ii) From Eq. (ii), we can rewrite Eq. (i) as dQ dt ∝r (r^2 )^2 or dQ dt ∝r^4

$A small sphere of radius r falls from rest in a viscous liquid. As a result, heat is produced due to viscous force. The rate of production of heat when the sphere attains its terminal velocity, is proportional to [NEET 2018]$

Solution

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