A shell of mass m is at rest initially. It explodes into three fragments having mass in the ratio 2: 2: 1. If the fragments having equal mass fly off…

A shell of mass $\displaystyle m$ is at rest initially. It explodes into three fragments having mass in the ratio $\displaystyle 2$ : $\displaystyle 2$ : 1. If the fragments having equal mass fly off along mutually perpendicular directions with speed $\displaystyle v$, the speed of the third (lighter) fragment is :