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JEE MainPhysicsCenter of Mass, Momentum and Collision

A system consists of two particles of masses 2 kg and 3 kg . The position vector of the centre of mass of the system is 2 i + j - k m . If the position vector of the 2 kg particle is - i + 4 j + 2 k m , then the position vector of the 3 kg particle is:

Options

  1. A12 i - 3 j - 9 k m
  2. B8 3 i + 13 3 j - 1 3 k m
  3. C3 i - 3 j - 3 k m
  4. D4 i - j - 3 k m

Correct answer

D. 4 i - j - 3 k m

Step-by-step solution

The position vector of the centre of mass for a two-particle system is given by: r _ com = m₁ r ₁ + m₂ r ₂ m₁ + m₂ Given values are: m₁ = 2 kg m₂ = 3 kg r _ com = 2 i + j - k r ₁ = - i + 4 j + 2 k Substituting the values into the formula: 2 i + j - k = 2(- i + 4 j + 2 k ) + 3 r ₂ 2 + 3 Multiplying both sides by the total mass ( 5 kg ): 10 i + 5 j - 5 k = -2 i + 8 j + 4 k + 3 r ₂ Rearranging to solve for 3 r ₂ : 3 r ₂ = (10 i + 5 j - 5 k ) - (-2 i + 8 j + 4 k ) 3 r ₂ = (10 + 2) i + (5 - 8) j + (-5 - 4) k 3 r ₂ = 12

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