Question

The blades of a wind mill sweep out a circle of area $A$. If wind flows with velocity $v$ perpendicular to blades of wind mill and its density is $\rho$, then the mechanical power received by wind mill is:

• A. $\frac{\rho A{v}^3}{8}$
• B. $\frac{\rho A{v}^3}{2}$
• C. $\rho A{v}^2$
• D. $2\rho A{v}^2$

Answer 1

The correct option is B $\frac{\rho A{v}^3}{2}$

The mass of air

$m=\rho .V=\rho Avt$

The K.E is

$K.E=\frac{1}{2}m{v}^2=\frac{1}{2}\rho Av{v}^2=\frac{1}{2}\rho A{v}^3$

The mechanical power received by wind mill is

$P=\frac{K.E}{t}=\frac{1}{2}\rho A{v}^3$