A bomb of mass `4 m` explodes into two parts of mass ratio `1 : 3`. If the `K.E`. Of smaller fragment is `K` , find the `K.E.` of the larger fragment.

Explanation

By momentum conservation ,
`0 = mv + 3mv' rArr v' = -(v)/(3)`
Given `K_(1) = (1)/(2) mv^(2) = K`
`K_(2) = (1)/(2) xx 3mv'^(2) = K'`
`(K')/(K) = 3(v'//v)^(2) = 3((1)/(3))^(2) = (1)/(3)`
`K' = (K)/(3)`
OR
Due to the momentum conservation , momentum of two pieces is equal and opposite.
`K = (p^(2))/(2m) , K' = (p^(2))/(2.3 m)`
`(K')/(K) = (1)/(3) rArr K' = (K)/(3)`
where `K' is the K.E.` of larger gragment.