An object with kinetic energy K explodes into two pieces, each of which moves with twice the speed of the original object.
Compare the internal and center-of-mass energies after the explosion.
3. The attempt at a solution
Let K1 be the kinetic energy of the main object before the explosion. k2 and k3 be the kinetic energies after explosion.
K1 = k2 + k3
Let K1 = 0.5m1v12 = K
0.5m1v12 = 0.5m2v22 + 0.5m3v32
and since each pieces has twice the velocity of the original piece befor explosion
0.5m1v2 = 0.5m2(2v)2 + 0.5m3(2v)2
∴ 0.5m1v2 = 0.5(4v2)(m2+m3)