The coordinates of centre of mass of a uniform flag shaped lamina… | JEE Main 2020 (8 Jan, Shift 1)

Q7JEE Main 2020 · 8 JAN · SHIFT 1Medium

Composite & Cut-Out Bodies

The coordinates of centre of mass of a uniform flag shaped lamina (thin flat plate) of mass 4kg. (The coordinates of the same are shown in figure) are:

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Answer: (a)

Split the flag into two rectangles of uniform density, so mass $\propto$ area.
Rectangle 1: $0\le x\le 1,\ 0\le y\le 3$ , area $3$ , centre $(0.5,\ 1.5)$ .
Rectangle 2: $1\le x\le 2,\ 2\le y\le 3$ , area $1$ , centre $(1.5,\ 2.5)$ .
$x_{cm} = \frac{3(0.5)+1(1.5)}{4} = 0.75$ m, $\ y_{cm} = \frac{3(1.5)+1(2.5)}{4} = 1.75$ m
So the answer is (a) $(0.75\text{ m},\ 1.75\text{ m})$ .

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