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

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Answer & Solution

Correct Answer

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

Step-by-step Solution

Detailed explanation

\(x = \frac{{M\frac{a}{2} - \frac{M}{4} \times \frac{{3a}}{4}}}{{M - \frac{M}{4}}}\)

\( = \frac{{\frac{a}{2} - \frac{{3a}}{{16}} \times \frac{{3a}}{4}}}{{\frac{3}{4}}} = \frac{{\frac{{5a}}{{16}}}}{{\frac{3}{4}}} = \frac{{5a}}{{12}}\)

\(y = \frac{{M\frac{b}{2} - \frac{M}{4} \times \frac{{3b}}{4}}}{{M - \frac{M}{4}}} = \frac{{5b}}{{12}}\)

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