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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:

1. r³
2. r²
3. r⁴
4. r⁵

Correct answer: r⁵

Solution

The rate of heat production due to viscous force is equal to the power dissipated, which is given by the product of the viscous force and terminal velocity. Using Stokes' law, the viscous force is proportional to r, and terminal velocity is proportional to r². Thus, the power (rate of heat production) is proportional to r × r² = r⁵.

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