An object of mass 2kg is dropped from a certain height.On rebounding from the ground,it rises vertically till 2/5th of its initial height. Find the ratio of magnitude of momentum of the object just before and after striking to ground.
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Momentum of the object = p
Kinetic energy = p² / (2m)
Kinetic energy just before or just after hitting the ground = Potential energy when the ball is on top = m g h
Reason : conservation of energy.
so p1² / (2m) = m g h1 So p1 = √(2gh1)
so p2² / (2m) = m g h2 = 2 mg h1/5 p2 = √(4gh1/5)
p1 / p2 = √5/√2
Kinetic energy = p² / (2m)
Kinetic energy just before or just after hitting the ground = Potential energy when the ball is on top = m g h
Reason : conservation of energy.
so p1² / (2m) = m g h1 So p1 = √(2gh1)
so p2² / (2m) = m g h2 = 2 mg h1/5 p2 = √(4gh1/5)
p1 / p2 = √5/√2
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