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JIPMER2016PhysicsCenter of Mass, Momentum and Collision

Particles of masses m, 2 m, 3 m, , n m are placed on the same line at distances L, 2 L, 3 L, , n L from O . The distance of centre of mass from O is

Options

  1. A(2 n+1) L 4
  2. BL (2 n+1)
  3. Cn (n^2+1 ) L 2
  4. D(2 n+1) L 3

Correct answer

D. (2 n+1) L 3

Step-by-step solution

x_ C M = mL+2 m 2 L+ +n m n L m+2 m+ +n m aligned & = L (1^2+2^2+ +n^2 ) (1+2+ +n) & =L n^2 n =L n(n+1)(2 n+1) 6 n(n+1) 2 & = (2 n+1) L 3 aligned

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