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A uniform rectangular thin sheet ABCD of mass M has length a and breadth b. If the top-right quarter (HBGO, where O is the centre) is cut off, the coordinates of the centre of mass of the remaining portion (with D at the origin) are

Asked in JEE Main 8th April 2nd Shift 2019 · Centre of mass by integration

• (1) ((5a)/3, (5b)/3)
• (2) ((2a)/3, (2b)/3)
• (3) ((3a)/4, (3b)/4)
• (4) ((5a)/(12), (5b)/(12))

Step-by-step solution

Why the other options are wrong

• (1) Comes from an arithmetic slip that multiplies the offset by 4/3 instead of dividing, giving values larger than the sheet.
• (2) Comes from treating the removed piece as half the sheet rather than a quarter.
• (3) Comes from reporting the centroid of the removed quarter ((3a)/4,(3b)/4) instead of the remaining part.

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