Level 1: Double the Wind Speed: Windmill Power ×4?
A water jet hitting a wall.
A horizontal water jet from a hose hits a wall and stops dead (it does not bounce back). If the water's speed is doubled through the same nozzle, the force on the wall becomes:
The force on the wall is the momentum the water loses each second. Each second a mass ρAv of water arrives, and each kilogram brings momentum v.
Doubling the speed doubles both the mass arriving each second and the momentum of each kilogram, so the force rises four times. Momentum flux goes as v², while kinetic-energy flux, the windmill's power, goes as v³.
Every Level 2 starts from a quick question, Level 1, and changes one thing. Seeing what that change does is the skill JEE Main tests. Try it here, free and with no signup, then read the worked answer.
