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NTA Abhyas JEE Main2020PhysicsCenter of Mass, Momentum and CollisionPractice

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

Options

  1. A2 n + 1 L 4
  2. BL 2 n + 1
  3. Cn n 2 + 1 L 2
  4. D2 n + 1 L 3

Correct answer

D. 2 n + 1 L 3

Step-by-step solution

L ∵ x C M = m L + 2 m × 2 L + … + n m × n L m + 2 m + … + n m = 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

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