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Question

# A surface is hit elastically and normally by n balls per unit time, all the balls having the same mass m and moving with the same velocity u. The force on the surface is:

A
mnu2
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B
2mnu2
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C
0.5mnu2
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D
2mnu
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Solution

## The correct option is D 2mnuVelocity of ball initially vi=u ^i Since the collision is elastic, thus the ball will move with same speed but in opposite direction after collision.Velocity of ball finally vf=−u ^i Change in momentum of each ball Δp=m(vf−vi)=−2mu ^iMagnitude of change in momentum of each ball |Δp|=2mu kg m/sNet rate of change in momentum of balls ΔpΔt=2mnuForce acting on the surface F=ΔpΔt=2mnu

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