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AP EAMCET202316 May 2023Morning ShiftPhysicsCenter of Mass, Momentum and CollisionActual

A circular plate A of radius 1.5 r is removed from one edge of a uniform circular plate B of radius 2 r . The distance of centre of mass of the remaining portion from the centre of the plate B is

Options

  1. A5 r 12
  2. B9 r 14
  3. C3 r 4
  4. D7 r 8

Correct answer

B. 9 r 14

Step-by-step solution

Radius of removed circular plate, A =1.5 r Radius of circular plate, B =2 r Let mass of circular plate A, M₁=M So surface mass density, = M (2 r)^2 = M 4 r^2 Then mass of removed circular plate, A aligned & M ₂= A & = M 4 r ^2 (1.5 r )^2 & = M 4 1.5 1.5=0.5625 M aligned The distance of centre of mass of the remaining portion from the centre of the plate B is aligned & X_ c m = M₁ x₁-M₂ x₂ M₁-M₂ & = M 0-0.5625 M 0.5 g M-0.5625 M = 9 r 14 aligned

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