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Question 30545
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Center of Mass, Momentum and Collision: COM — Missing Piece MCQ

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COM — Missing PieceHardQuestion 30545

Question

A disc (radius R, mass M) has a circular hole (radius R/2) cut off-centre. If the hole centre is at R/2 from disc centre, the COM of the remaining piece from original centre is:
  1. A
    R/6 away from hole
  2. B
    R/6 toward the hole side
    Correct
  3. C
    R/2
  4. D
    0 (centre unchanged)

Correct answer

R/6 toward the hole side

Explanation

Mass of removed disc = M/4 (proportional to area, i.e., (R/2)²/R² = 1/4). x_cm_removed = R/2. x_cm × (3M/4) + (R/2)(M/4) = 0 (original at 0). x_cm = −(M/4)(R/2)/(3M/4) = −R/6 (away from hole means toward the heavy side).

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