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Question:

A uniform rectangular thin sheet ABCD of mass M has length a and breadth b, as shown in the figure. If the shaded portion HBGO is cut-off, the coordinates of the centre of mass of the remaining portion will be :-

(2a/3,2b/3)

(5a/3,5b/3)

(3a/4,3b/4)

(5a/12,5b/12)

Solution:

Correct option is D (5a/12,5b/12)
x = (Ma/2 - M/4 × 3a/4) / (M - M/4) = (a/2 - 3a/16) / (3/4) = (5a/16) / (3/4) = 5a/12
y = (Mb/2 - M/4 × 3b/4) / (M - M/4) = 5b/12