Question

A light and a heavy object have the same momentum. Find out the ratio of their kinetic energies ?

Answer 1

Let the two bodies have masses m1 and m2 respectively such that m2 > m1 . Then, for first object p1 = m1v1 and for second object p2 = m2v2
But p1 = p2 or m1v1 = m2v2
Since m1 < m2, then v1 > v2
Now, K = 1/2 mv^2 = 1/2 pv, therefore,
K1/K2 = p1v1 / p2v2 = v1/v2
But v1 > v2
Therefore, kinetic energy of body of lesser mass is more.