Question

Two bodies of mass m and M have the same linear momentum. What is the ratio of their kinetic energies?

Answer 1

As we know the relation b/w P and KE.

i.e KE=P^2/2m              {P=mv.......(1)

                                            KE=1/2mv^2..............(2)

                                               Squaring on both sides of eqn 1

                                               P^2=(mv)^2

                                              v^2=P^2/m^2 .............(3)

                                                substituting (3) in (2)  we get KE=P^2/2m}

       Since , P is same , KE is inversely proportional to mass.

Taking KE of m=KE1; KE of M= KE2.

       so KE1/KE2=M/m   .