Question

Two bodies of mass m1 and m2 have same kinetic energy the ratio of their momentum is

Answer 1

let E be the kinetic energy of the two bodies
then their momentums are √2m1E and √2m2E respectively
then ratio of their momentums=(√m1)/(√m2)
I.e. √m1 : √m2

Answer 2

Given: Two bodies of mass m₁ and m₂ have same kinetic energy.

To find: the ratio of their momentum.

Solution: We know by the relationship between kinetic energy and momentum that:

               K.E. = p²/ 2m _____(1)

We use the above relation to find the ratio of their momentum.

Kinetic energies of the masses are equal implying:

              K.E.₁ = K.E.₂ = K.E. _____(2)

From (1) and (2) and as per the question:

                K.E.₁ = K.E.₂

               p₁²/ 2m₁ = p₂²/ 2m₂

                p₁²/ p₂² = m₁ / m₂

                p₁ / p₂ = √m₁ / √m₂

Hence, the ratio of the momentum is √m₁ : √m₂.