If two particles have equal kinetic energies, are their momenta necessarily equal? explain.

No the given statement is not necessarily true.

Explanation:

We know that the kinetic energy of a particle of mass 'm' moving with velocity 'v' is given by

Similarly the momentum is given by

For 2 particles with masses and moving with velocities respectively the respective kinetic energies is given by

Similarly For 2 particles with masses and moving with velocities respectively the respective momenta are given by

Now since it is given that the two kinetic energies are equal thus we have

Thus we infer that the moumenta are not equal since the ratio on right of 'i' is not 1 , and can be 1 only if the velocities of the 2 particles are equal which becomes a special case and not a general case.

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