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) $\sqrt2\ v$