# A light and a heavy body have the same momentum.Which one has larger kinetic energy?

Lighter object: This is because if lighter and heavier object have equal momentum then it is clear that lighter object has greater velocity & since K.E. is velocity dominant so the lighter object with greater velocity will have greater K.E.

Linear momentum of lighter object = p1=m1v1

Linear momentum of heavier object = p2=m2v2

Given p1 = p2 ———(i)

Given, m1 v1 > v2 ————(ii)

Now, KE = ½ mv^2 = ½ m v x v = 1/2 pv

From (i) & (ii) p1v1 > p2v2 => ½ p1v1 > ½ p2v2 => KE1> KE2