The KE of a body becomes 2 times of its original value then the new momentum will be more than its initial momentum by

√2

Explanation:

If the final kinetic energy is 2 times the initial kinetic energy:

KE = 2 KE₀

½ mv² = 2 (½ mv₀²)

v² = 2 v₀²

v = √2 v₀

Therefore, the ratio of the final momentum to the initial momentum is:

p / p₀

mv / (mv₀)

v / v₀

√2