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 along mutually perpendicular directions with speed $v$, the speed of the third (lighter) fragment is :

(1) $2\sqrt2\ v$

(2) $3\sqrt2\ v$

(3) $v$

(4) $\sqrt2\ v$

(1) $2\sqrt2\ v$

(2) $3\sqrt2\ v$

(3) $v$

(4) $\sqrt2\ v$