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Highly selective Backlog Qs for JEE MainPhysicsCenter of Mass, Momentum and Collision

Centre of mass (C.M.) of three particles of masses 1 ~kg , 2 ~kg and 3 ~kg lies at the point (1,2,3) and C.M. of another system of particles of 3 ~kg and 2 ~kg lies at the point (-1,3,-2) . Where should we put a particle of mass 5 ~kg so that the C.M. of entire system lies at the C.M. of the first system ?

Options

  1. A(3,1,8)
  2. B(0,0,0)
  3. C(1,3,2)
  4. D(-1,2,3)

Correct answer

A. (3,1,8)

Step-by-step solution

. array l 6 ~kg [1,2,3] 5 ~kg [-1,3,-2] 5 ~kg [ x , y , z ] array ) ( x , y , z )=(1,2,3) x = m₁ x₁+m₂ x₂ m₁+m₂ 1= 5(-1)+5 x 10 -5+5 x=10 x=3 y =2= 5 3+5 y 10 , 15+5 y=20, y=1 z =3= 5(-2)+5 . z 10 ,-10+5 z=30, z=8

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