An object of mass $3\,m$ splits into three equal fragments. Two fragments have velocities $v\hat j$ and $v\hat i$. The velocity of the third fragment is

  • A

    $v(\hat j - \hat i)$

  • B

    $v(\hat i - \hat j)$

  • C

    $ - v(\hat i + \hat j)$

  • D

    $\frac{{v(\hat i + \hat j)}}{{\sqrt 2 }}$

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