Question

Two bodies are moving with same kinetic energy and their masses are in the ratio of 1:2 . The ratio of their velocities is?

Answer 1

The ratio will be 2:1

Answer 2

K.E. = mv^2/2 = (mv)^2/2m = p^2/2m.  

If mass and momentum of first are m & p, and of second are M & P then

p^2/2m = P^2/2M  thus p^2/P^2 = 2m/2M

or p/P = sqrt(m/M) = sqrt(2/4) = sqrt(1/2)