Question

What happens to momentum when kinetic energy is doubled

Answer 1

If the momentum of an object is doubled, but its mass does not increase (so velocity remains well below the speed of light), then its velocity is doubled. If the velocity is doubled then the kinetic energy increases by the square of 2, or four time. Hence kinetic energy of the body will be 4 times to its eirlier value.

Answer 2

K directly proportional to p²

K/ 2K = (p/p')²

1 / √2 = p / p'

p' = √2 p

Momentum becomes √2 times.