A uniform rectangular thin sheet ABCD of mass M has length a and… | JEE Main 2019 (8 Apr, Shift 2)

Q11JEE Main 2019 · 8 APR · SHIFT 2Medium

Composite & Cut-Out Bodies

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: (c)

Full sheet: mass $M$ at $\left(\frac{a}{2}, \frac{b}{2}\right)$ . Cut part HBGO is a quarter: mass $\frac{M}{4}$ at $\left(\frac{3a}{4}, \frac{3b}{4}\right)$ .
$x_{cm} = \frac{M\frac{a}{2} - \frac{M}{4}\cdot\frac{3a}{4}}{\frac{3M}{4}} = \frac{\frac{5a}{16}}{\frac{3}{4}} = \frac{5a}{12}$
By the same working $y_{cm} = \frac{5b}{12}$ .
So the answer is (c) $\left(\frac{5a}{12}, \frac{5b}{12}\right)$ .

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