Question

two bodies of masses 1kg and 4 kg having same k.e find the ration of their momentum

Answer 1

Dear student,

It is given that the two bodies m₁ and m₂ have masses 1 kg and 4 kg respectively. These masses have the same kinetic energy, i.e.

            K.E.₁ = K.E.₂ ______(1)

We need to find the ratio of their momentum.

Now, we know by the relationship between momentum and kinetic energy that;

                  K.E. = p² / 2m ______(2)

where, K.E. = kinetic energy

               p = momentum

               m = mass

Using the above relation for the given masses, we have;

              K.E.₁ = K.E.₂

        p₁²/ 2m₁ = p₂² / 2m₂

          p₁²/ p₂² = 2m₁ / 2m₂

          p₁²/ p₂² = 2 × 1/ 4× 2

          p₁²/ p₂² = 2/ 8

          p₁²/ p₂² = 1/ 4

             p₁/ p₂ = √ 1/ 4

             p₁/ p₂ = 1/2

Hence, the ratio of their momentum is 1 : 2.