An unstable particle is at rest and suddenly decays into two

An unstable particle is at rest and suddenly decays into two fragments. No external forces act on the particle or its fragments. One of the fragments has a speed of 0.40c and a mass of 6.68×1027kg, while the other has a mass of 1.67×1027kg.

What is the speed of the less massive fragment?

Solution

since no external force acts so there is no change in momentum of the system

since initially the particle was at rest so initial momentum = 0

as no external force acts

initial momentum = final momentum

0 = 6.68 x 10^-27 x 0.40 c + 1.67 x 10^-27 x v [where v = velocity of the less massive fragment]

v = - 1.6 c

therefore speed of the less massive fragment = 1.6 c