Question

Two bodies of masses m and 2m have same momentum. their respective kinetic energies and are in the ratio:

Answer 1

K.E = 1/2mv*mv
mass1 = m
mass2 = 21
Then, K.E of mass1 = 1/2mv*mv
and K.E of mass2= 1/2*2mv*2mv
Then divide K.E of mass1 and mass2
So,(1/2mv*mv)/(1/2*2mv*2mv)
We get, 1/4
Then ratio = 1:4

Answer 2

Let the momentum of the two bodies of mass m and 2m be P1 and P2, respectively.

P = mv (mass × velocity)
So, P1 = (mv) N.s
P2 = (2mv) N.s

Now, Kinetic energy (E) = ½mv^2 = ½(mv)v = ½Pv

So, E1 = ½(mv)v = ½mv^2
E2 = ½(2mv)v = mv^2

Ratio = E1/E2 = (½mv^2)/(mv^2) = ½/1 = 1:2

Therefore, the ratio of kinetic energise is 1:2.