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. (a) `V`
B. (b) `V^2`
C. (c) `V^3`
D. (d) `V^4`

Answer

C

Explanation

Number of particles striking the blades/time `prop` velocity of wind
`KE of particle prop (Velocity of wind)^2`
`:. Power output prop (Number of particles striking//time) xx (KE of particle) prop V^3`
Alternative method:
`F=v((dm)/(dt))=v(d)/(dt)=(rhoxxvolume)`
`=vrho(d)/(dt)(volume)=vrhoxx(Av)=Arhov^2`
`Power=Force xx Velocity =Arhov^2xxv=Arhov^3impliesP prop v^3`