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AP EAMCET20228 Jul 2022Evening ShiftPhysicsCenter of Mass, Momentum and CollisionActual

A circular portion of radius R₂ has been removed from one edge of a circular disc of radius R₁ . The correct expression for the centre of mass for the remaining portion of the disc is

Options

  1. A- R₂^2 R₁+R₂
  2. B- R₂^2 R₁-R₂
  3. CR₂^2 R₁+R₂
  4. D- R₁^2 R₁+R₂

Correct answer

A. - R₂^2 R₁+R₂

Step-by-step solution

Given situation is shown below. Here we treat removed mass as negative mass. As solid is symmetrical about X - axis, its CM lies along X - axis. Now x_ CM = m₁ x₁-m₂ x₂ m₁-m₂ = d R₁^2 0-d R₂^2 (R₁-R₂ ) d R₁^2-d R₂^2 Here, d= Area wise mass density x_ CM = -R₂^2 (R₁-R₂ ) R₁^2-R₂^2 = -R₂^2 (R₁-R₂ ) (R₁+R₂ ) (R₁-R₂ ) = -R₂^2 R₁+R₂^

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