# 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: Option 1) $\left ( \frac{3a}{4}, \frac{3b}{4} \right )$ Option 2) $\left ( \frac{5a}{3}, \frac{5b}{3} \right )$ Option 3) $\left ( \frac{2a}{3}, \frac{2b}{3} \right )$ Option 4) $\left ( \frac{5a}{12}, \frac{5b}{12} \right )$

$X_{cm}=\frac{(ab) \times \frac{a}{2}-(\frac{3a}{4})\times \frac{ab}{4}}{(ab)-\frac{ab}{4}}=\frac{a[\frac{1}{2}-\frac{3}{16}]}{1-\frac{1}{4}}=\frac{a[\frac{5}{16}]}{\frac{3}{4}}=\frac{5a}{12}$

$Y_{cm}=\frac{(ab) \times \frac{b}{2}-(\frac{3b}{4})\times \frac{ab}{4}}{(ab)-\frac{ab}{4}}=\frac{b[\frac{1}{2}-\frac{3}{16}]}{1-\frac{1}{4}}=\frac{b[\frac{5}{16}]}{\frac{3}{4}}=\frac{5b}{12}$

Option 1)

$\left ( \frac{3a}{4}, \frac{3b}{4} \right )$

Option 2)

$\left ( \frac{5a}{3}, \frac{5b}{3} \right )$

Option 3)

$\left ( \frac{2a}{3}, \frac{2b}{3} \right )$

Option 4)

$\left ( \frac{5a}{12}, \frac{5b}{12} \right )$

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