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 - Physics MCQ NEET (UG) 2018 2026 | ExamTest.live

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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:

Solution & Step-by-step Explanation

1. Rate of production of heat = Power (P) = F \times v .2. At terminal velocity, F (Viscous force) = 6 π ηr v_{t} .3. Terminal velocity v_{t} \propto r^{2} .4. So, P = (6 π ηr v_{t}) \times v_{t} = 6 π ηr v_{t}^{2} .5. Substituting v_{t} \propto r^{2} : P \propto r \times (r^{2})^{2} ⟹ P \propto r^{5}

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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:

r^{5}

r^{2}

r^{3}

r^{4}

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