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AP EAMCET2011PhysicsCenter of Mass, Momentum and Collision

A circular disc of radius R is removed from a bigger circular disc of radius 2 R such that the circumferences of the discs touch. The centre of mass of the new disc is at a distance R from the centre of the bigger disc. The value of is

Options

  1. A1 2
  2. B1 3
  3. C1 4
  4. D1 6

Correct answer

B. 1 3

Step-by-step solution

Let centre O₁ of disc be the origin. Due to symmetry the centre of mass of remaining part will lie at x -axis. Let CM of new disc is at point O ₂ where, O ₁ O ₂= R (given). here mass of cut off portion, m= (R)^2 M (2 R)^2 = M 4 and position of its centre of mass, O₁ O₁=R Hence, for remaining part (new disc) aligned x_ CM = R & = M 0- ( M 4 ) R M- M 4 & =- R 3 = 1 3 aligned

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