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

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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) \( 3 \sqrt{2} \mathrm{v} \)
(2) \( \mathrm{v} \)
(3) \( \sqrt{2} \mathrm{v} \)
(4) \( 2 \sqrt{2} \mathrm{v} \)
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