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      Question

      A bomb at rest explodes into two pieces of unequal

      masses. Which of the following is necessarily true about the motion of the fragments?
      A Heavier fragment moves faster Correct Answer Incorrect Answer
      B Both fragments move with equal speed Correct Answer Incorrect Answer
      C Total momentum of system remains zero Correct Answer Incorrect Answer
      D Both have equal kinetic energy Correct Answer Incorrect Answer

      Solution

      When a bomb at rest explodes into two pieces, momentum is conserved . Initially, the total momentum is zero , so after the explosion, the vector sum of the momenta of the two fragments must also be zero . Let:

      • Masses of fragments = m1​ and m2
      • Velocities after explosion = v1​ and v2
      From conservation of linear momentum: m1​ v1+ m2 v2=0 ⇒ m1​ v1 = − m2 v2​ This implies:
      • The momenta are equal and opposite.
      • The heavier fragment will have lower speed than the lighter one to maintain this equality.
      But more importantly, the total momentum remains zero even though the individual momenta are nonzero and opposite.

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