Question

An object initially at rest breaks into two pieces as the result of an explosion. One piece has twice the kinetic energy of the other piece. What is the ratio of the masses of the two pieces? Which piece has the larger mass?

Answer 1

Energy conservation law: m1v1^2/2+m2v2^2/2=0
Impulse conservation law: m1v1=m2v2
m1v1^2/m2v2^2=2 (from the task)
v1/v2=2
m1v1=m2v2
m1v1=2m2v2
m1=2m2
So, body with bigger kinetic energy has two times biggermass.