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NEET2019PhysicsCenter of Mass, Momentum and CollisionActual

An object flying in air with velocity (20 i +25 j -12 k ) suddenly breaks in two pieces whose masses are in the ratio 1: 5 . The smaller mass flies off with a velocity (100 i +35 j +8 k ) . The velocity of the larger piece will be

Options

  1. A4 i +23 j -8 k
  2. B-100 i -35 j -8 k
  3. C20 i +15 j -80 k
  4. D-20 i -15 j -80 k

Correct answer

A. 4 i +23 j -8 k

Step-by-step solution

Let m be the mass of an object flying with velocity v in air. When it split into two pieces of masses in ratio 1: 5 , the mass of smaller piece is m / 6 and of bigger piece is 5 ~m 6 . This situation can be interpreted diagrammatically as below As the object breaks in two pieces, so the momentum of the system will remains conserved i.e. the total momentum (before breaking) = total momentum (after breaking) aligned & mv = m 6 v ₁+ 5 ~m 6 v ₂ v = v ₁ 6 + 5 v ₂ 6 & Here, aligned v & =20 i +25 j -12 k v ₁ & =100 i +35

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