Question

How does the kinetic energy of a body change if momentum is double?

Answer 1

$KE = \frac{p^{2} }{2m}\\\\KE = \frac{(2p)^{2} }{2m}\\ \\KE = 4\frac{p^{2} }{2m}$

Kinetic energy becomes four times the original.

Answer 2

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 .