How does the kinetic energy of a body change if momentum is double?
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Kinetic energy becomes four times the original.
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We know the Relation,
K.E. = p²/2m
∴ Initial Kinetic Energy (K.E. ₁)= p²/2m ------eq(ii)
Now, If the Momentum, p will be doubled, then
K.E.₂ = (2p)²/2m
⇒ K.E.₂ = 4p²/2m
⇒ K.E.₂ = 4 (K.E.₁)
This means that if the momentum will be doubled then the kinetic energy will become four times that of the initial.
Hope it helps .
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