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Manipal MET2015PhysicsCenter of Mass, Momentum and Collision

Two point masses 1 and 2 move with uniform velocities v ₁ and v ₂ respectively. Their initial position vectors are r ₁ and r ₂ , respectively. Which of the following should be satisfied for the collision of the point masses?

Options

  1. Ar₁-r₂ |r₂-r₁ | = v₂-v₁ |v₂-v₁ |
  2. Br₂-r₁ |r₁-r₁ | = v₂-v₁ |v₂-v₁ |
  3. Cr₂-r₁ |r₂+r₁ | = v₂-v₁ |v₂+v₁ |
  4. Dr₂+r₁ |r₂+r₁ | = v₂-v₁ |v₂+v₁ |

Correct answer

A. r₁-r₂ |r₂-r₁ | = v₂-v₁ |v₂-v₁ |

Step-by-step solution

array ll For collision, & r ₁+ v ₁ t= r ₂+ v ₂ t & r ₁- r ₂= ( v ₂- v ₁ ) t array Equating unit vectors, we get r₁-r₂ |r₂-r₁ | = v₁-v₂ |v₂-v₁ |

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