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  4. n small balls, each of mass m impinge elastically each second on a surface with a velocity u , then the force experienced by the surface in one second, will be:

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Q. $ n $ small balls, each of mass $ m $ impinge elastically each second on a surface with a velocity $ u $ , then the force experienced by the surface in one second, will be:

BHUBHU 2001Work, Energy and Power

Solution:

Force experienced by the surface is equal to change in momentum in one second.
From Newton's second law of motion the rate of change of momentum of a body is equal to the external force applied on the body and the change is momentum always takes place in the direction of the force.
Momentum of ball before inpact $=m u$
Momentum after inpact $=-m u$
Change in momentum $=m u-(-m u)=2 \,m u$.
Change in momentum due to $n$ balls in one
second is $=2\, mnu$.
Change of momentum $=$ Force experienced per second
$=2\, mnu$