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Physics · WORK, ENERGY AND POWER
हिन्दीA windmill sweeps out a circle of area \( A = 30\text{ m}^2 \). The wind blows perpendicular to the circle with a constant velocity \( v = 36\text{ km h}^{-1} \). Assuming the density of air is \( \rho = 1.2\text{ kg m}^{-3} \) and the windmill converts \( 25\% \) of the wind's available kinetic energy into electrical energy, the electrical power produced is:
Correct answer · Option 4
\( 4.5\text{ kW} \)
Explanation
Velocity \( v = 36\text{ km/h} = 10\text{ m/s} \). Total kinetic energy per second is \( P_{\text{wind}} = \frac{1}{2} \rho A v^3 = \frac{1}{2} \times 1.2 \times 30 \times 10^3 = 18000\text{ W} = 18\text{ kW} \). Electrical power \( P_{\text{elec}} = 0.25 \times 18\text{ kW} = 4.5\text{ kW} \).
