A wind - powered generator converts wind energy into electrical energy . Assume that the generator convents a fixed fraction of the wind energy intercepted by to blades into electrical energy for wind speed `V` , the electrical power output will be propertional to

Options

A. V
B. `V^2`
C. `V^3`
D. `V^4`

Answer

C

Explanation

Number of particles striking the blades/time `prop` velocity of wind KE of particle `prop ("Velocity of wi nd")^2`
`:. "Power output" prop ("Number of particl e s striki ng/time") xx ("KE of partic l e") V^3`
Alternative method:
`F = v((dm)/(dt)) = v (d)/(dt) (rho xx "volume") " " = vrho(d)/(dt) ("volume") = vrho xx (Av) = Arho v^2`
Power = Force `xx` velocity `" " = A rho v^2 xx v = A rho v^3 implies P prop v^3`.