[UPSC CSE 2013] Special Theory of Relativity (Q367, 15M)

A particle of rest mass M=4\times10^{-27}\ \mathrm{kg}, disintegrates into two particles of rest masses M_1=3\times10^{-27}\ \mathrm{kg} and M_2=1\times10^{-27}\ \mathrm{kg}. Show that the energies E_1 and E_2 of these two parts after disintegration satisfy the condition E_1=3E_2 while moving in opposite directions with equal linear momenta. Give necessary mathematical derivation.