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Physics · MECHANICAL PROPERTIES OF FLUIDS
हिन्दीA small spherical lead ball of radius \( a \) and density \( \rho \) falls freely under gravity in a viscous fluid of density \( \sigma \) and coefficient of viscosity \( \eta \). If its terminal velocity is \( v_{\text{t}} \), the rate of production of heat due to viscous dissipation in steady state is proportional to:
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Correct answer · Option D
\( a^5 \)
Explanation
The rate of heat generation is \( \frac{dQ}{dt} = F_{\text{v}} v_{\text{t}} = (6\pi\eta a v_{\text{t}}) v_{\text{t}} \). Since \( v_{\text{t}} \propto a^2 \), we get \( \frac{dQ}{dt} \propto a \cdot (a^2)^2 = a^5 \).
