Q 11-06-184JEE MainJEE Main 2020 (8 Jan, Shift 1)Easy
The coordinates of the centre of mass of a uniform flag-shaped lamina (thin flat plate) of mass $4$ kg are: (The coordinates of the corners are shown in the figure, in metres.)
Answer: (B) $(0.75\ \text{m}, 1.75\ \text{m})$
Split the lamina into two rectangles:
Pole: $0 \le x \le 1$, $0 \le y \le 3$, area $3$, centre $(0.5, 1.5)$.
Flag: $1 \le x \le 2$, $2 \le y \le 3$, area $1$, centre $(1.5, 2.5)$.
$$x_{cm} = \frac{3(0.5) + 1(1.5)}{4} = 0.75\ \text{m}, \qquad y_{cm} = \frac{3(1.5) + 1(2.5)}{4} = 1.75\ \text{m}$$
Solution by Sreeraj P, M.Sc Physics