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99 Percentile Qs Bank for JEE MainPhysicsCenter of Mass, Momentum and Collision

A small disc of the radius 2   cm is cut from a disc of radius 6   cm . If the distance between their centres is 3 . 2   cm , what is the shift in the centre of mass of the disc?

Options

  1. A0 . 4   cm .
  2. B2 . 4   cm .
  3. C1 . 8   cm .
  4. D1 . 2   cm .

Correct answer

A. 0 . 4   cm .

Step-by-step solution

The situation is as below: Let the radius of the complete disc is a , and that of the small disc is b . Also, let the centre of mass now shift to O 2 at a distance x 2 from the original centre. (Let us consider the origin to be at O .) The position of the new centre of mass is given by: X C M = m c x c +   m 1 x 1 m c +   m 1 Where, m c = mass of complete disc, x c = position of the centre of the disc which is 0 , m 1 = mass of cut out, x 1 = position of the centre of cut out. X C M = - σ π b 2

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