# A light and a heavy object have the same momentum, find out the ratio of their kinetic energies. Which one has a larger kinetic energy?

#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.

#2

Let m1 and m2 be the masses of the light and heavy objects respectively
We know that, K.E= p^2/2m
Therefore, K.E of light object= p^2/2m1
of heavy object= p^2/2m2
So, ratio- K.E1/K.E2
= p^2/2m1 * 2m1/p^2
P^2 gets cancelled as objects have same momentum
2 also gets cancelled
= m2/m1
Therefore ratio of their kinetic energies = mass of heavy object : mass of light object
Now K.E = 1/2mv^2
Therefore, K.E is directly proportional to mass.
Hence, K.E of heavy object will be greater than that of the light object
Prasanna you are wrong because you cannot take mv^2 as p
Because it is m* v^2
And not (mv)^2