Kinetic Energy of an object when it explodes?

Question

An object with mass m and speed v explodes into two pieces, one three times as massive as the other; the explosion takes place in gravity-free space. The less massive piece comes to rest. How much kinetic energy was added to the system?

Answer 1

(1/4)mv1 = (3/4)m(v2 - v1)
v1 = 3v2 - 3v1
v2 = (4/3)v1
∆KE = (1/2)mv1^2[(3/4)(4/3)^2 - 1]
∆KE = (1/3)KE1

Answer 2

5

Answer 3

Kinetic potential includes mass and speed. to that end if the speed of the two fragments are the comparable then the fragment m1 could have a mass thrice better than fragment m2.