Question

when the kinetic energy of a particle is increased by 300% then the momentum of the of the body is increased by how much?

Answer 1

Kinetic energy and momentum are related as
K = p²/(2m)

For an object of mass m
K ∝ p²
K₂/K₁ = (p₂/p₁)² ....(1)

Let’s say initial kinetic energy and momentum be 100% each
Then, equation (1) will become
(400% / 100%) = (p₂/100%)²
2 = p₂/(100%)
p₂ = 200%

Change in momentum = p₂ - p₁ = 200% - 100% = 100%

∴ Momentum is increased by 100%

Answer 2

Answer: 100%

Explanation:

When increasing by 300% kinetic energy becomes 4k.

Thus increase in momentum becomes

(((2k-k)/k)*100)%

=> 100% increase