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An object is moving though air at a spee...

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)

A

`2Av`

B

`2Av^2`

C

`2Av^(1/2)`

D

Can't be determined

Text Solution

Verified by Experts

The correct Answer is:
(B)
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)`
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