A wind - powered generator converts wind energy into electric energy. Assume that the energy intercepted by its blades into electrical energy. For wind speed v, the electrical power output will be proportional to,

Options

A. v
B. `v^(2)`
C. `v^(3)`
D. `v^(4)`

Answer

C

Explanation

`K.E=(1)/(2)mv^(2)`
`=(1)/(2)xx` density `xx` volume `xxv^(2)`
`=(1)/(2)xxrhoxxAxx x xx v^(2)`
Power = `(K.E)/("time")implies((1)/(2)rhoAxv^(2))/((x)/(v))`
`[v=(x)/(t),t=(x)/(v)]=(1)/(2)rhoAv^(3)`