A body of mass `1 kg` initially at rest, explodes and breaks into three fragments of masses in the ratio `1 : 1 : 3`. The two pieces of equal mass fly off perpendicular to each other with a speed of `15 m s^(-1)` each. What is the velocity of the heavier fragment?

Options

A. `5sqrt(2)m//s`
B. 45 m/s
C. 5 m/s
D. 156 m/s

Explanation

Conservation of momentum yields `vec(p)_("finall")=vec(p)_("initial")`, where `|vec(p)_("initial")|=(3m+m+m)0=0` and `p_("final")=|3m vec(v).+m vec(v)_(1)+m vec(v)_(2)|`
`rArr |3m vec(v).+m vec(v)_(1)+m vec(v)_(2)|=0`
`rArr 3mv. = m sqrt(v_(1)^(2)+v_(1)^(2)) " " (because vec(v)_(1)_|_ v_(2))`
`rArr v.=(sqrt(2)v)/(3) " " (because v_(1)=v_(2)=v)`
`rArr v.=(sqrt(2)xx15)/(3)=5sqrt(2)m//s`.