An object is moving though air at a speed v. If the area of the object normal to the direction of velocity is A and assuming elastic collision with air molecules, then the resistive force on the object is propotional to-(assume that molecules striking the object were initially at rest)

Options

A. `2Av`
B. `2Av^2`
C. `2Av^(1/2)`
D. Can't be determined

Answer

(B)

Explanation

Velocity of air molecule after collision `=2v`. The number of air-molecules accelerated to a velocity 2v in time `Deltat` is propotional to `AvDeltat`. Therefore `F=(Deltap)/(Deltat) prop(AvDeltat)((2v)/(Deltat))rArrFprop2Av^(2)`