A body of mass $M$ at rest explodes into three pieces, in the ratio of masses $1: 1: 2$. Two smaller pieces fly off perpendicular to each other with velocities of $30 \,ms ^{-1}$ and $40 \,ms ^{-1}$ respectively. The velocity of the third piece will be ............... $\,ms ^{-1}$

  • [JEE MAIN 2022]
  • A

    $15$

  • B

    $25$

  • C

    $35$

  • D

    $50$

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