A shell of mass \( m \) is at rest initially. It explodes into three fragments having masses in ...

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A shell of mass \( m \) is at rest initially. It explodes into three fragments having masses in the ratio \( 2: 2: 1 \). The fragments having equal masses fly off along mutually perpendicular directions with speed \( v \). What will be the speed of the third (lighter) fragment ?
(A) \( v \)
(B) \( \sqrt{2} v \)
(C) \( 2 \sqrt{2} v \)
(D) \( 3 \sqrt{2} v \)
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