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BITSAT2024PhysicsCenter of Mass, Momentum and CollisionActual

Two bodies of mass 1 kg and 3 kg have position vectors i +2 j +k and -3 i -2 j + k respectively. The magnitude of position vector of centre of mass of this system will be similar to the magnitude of vector :

Options

  1. Ai -2 j + k
  2. B-3 i -2 j + k
  3. C-2 i +2 k
  4. D-2 i - j +2 k

Correct answer

A. i -2 j + k

Step-by-step solution

Position of COM of a mass - system is given as, r _ com = m₁ r ₁+m₂ r ₂ m₁+m₂ = 1( i +2 j + k )+3(-3 i -2 j + k 1+3 =-2 i - j + k | r _ c m |=|-2 i - j + k |= (2)^2+(1)^2+(1)^2 = 6 Only option (1) magnitude is 1^2+(-2)^2+1^2 = 6 So option (1) is correct.

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