Q.
The coordinates of centre of mass of a uniform flag shaped lamina (thin flat plate) of mass $4\, kg$. (The coordinates of the same are shown in figure) are :
Solution:
$m_{1}=3\,kg
m_{2}=1\,kg$
Mass of plate-1 is assumed to be concentratedat $\left(0.5, 1.5\right)$
Mass of plate-2 is assumed to be concentratedat $\left(1.5, 2.5\right).$
$x_{cm}=\frac{m_{1}x_{1}+m_{2}x_{2}}{m_{1}+m_{2}}=\frac{3\times0.5+1\times1.5}{4}=0.75$
$y_{cm}=\frac{m_{1}y_{1}+m_{2}y_{2}}{m_{1}+m_{2}}=\frac{3\times 0.5+1\times 1.5}{4}=0.75$
