Question

If momentum of an object is increased by 20% then its kinetic energy will incease by

Answer 1

we know kinetic energy = p²/2m
if momentum is increased by 20%
so final momentum is 120% of p
= 120/100 of p = 6/5 of p
= 6p/5

therefore, E = (6p/5)² / 2m
E = (36p²/25) / 2m
E = 36/25 * p²/2m

increase in energy = 36/25 * p²/2m - p²/2m
= 11/25 * p²/2m
in percent = 44%

Answer 2

Hey there
If momentum of body increases by 20%,we meant that velocity of body increases by 20% because momentum is Maas ×velocity ,and mass remains constant for a body so,if we consider the original velocity be v ,then new velocity will be (v+20/100v=6/5v
Original kinetic energy of the body=1/2mv^2 and
new kinetic energy=1/2m(6/5 v)^2
=1/2mv^2(36/25)
Change in kinetic energy=1/2mv^2(36/25-1)
=1/2mv^2(11/25)
Also, original value of kinetic energy=1/2mv^2
Change%in kinetic energy
=(Change in kinetic energy/original value of kinetic energy×100)
=[1/2mv^2(11/25)]/(1/2mv^2)×100
=11/25×100%=44%.
Hence, kinetic energy will increase by 44%.Hope it helps