A body at rest breaks up into $3$ parts. If $2$ parts having equal masses fly off perpendicularly each after with a velocity of $12m/s$, then the velocity of the third part which has $3$ times mass of each part is

  • A

    $4\sqrt 2 \,m/s$ at an angle of ${45^o}$ from each body

  • B

    $24\sqrt 2 \,m/s$ at an angle of ${135^o}$from each body

  • C

    $6\sqrt 2 \,m/s$ at ${135^o}$from each body

  • D

    $4\sqrt 2 \,m/s$ at ${135^o}$ from each body

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