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 :

  • [NEET 2022]
  • A

    $\sqrt{2} v$

  • B

    $2 \sqrt{2} v$

  • C

    $3 \sqrt{2} v$

  • D

    $v$

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