A wind generator converts a fixed fraction of the kinetic energy of wind crossing its blade area into electricity. If speed is v and output power ∝vˣ, find x.
Physics · Mixed Chapter
JEE Main Practice

Question

A wind generator converts a fixed fraction of the kinetic energy of wind crossing its blade area into electricity. If speed is v and output power ∝vˣ, find x.

G1 Physics · Accepted Answer

Step 1: Mass flux through blade area A is ṁ=ρAv. Step 2: Each kilogram carries kinetic energy ½v², so available power is P=½ṁv². Step 3: Substitute: P=½ρAv³. Constant conversion efficiency preserves exponent 3. Thus x=3.