A uniform L-shaped lamina (a thin flat plate) of mass 3 kg consists of three identical squares each

Question

A uniform L-shaped lamina (a thin flat plate) of mass 3 kg consists of three identical squares each of side 1 m. The vertices of the lamina are at $(0,0)$, $(2,0)$, $(2,1)$, $(1,1)$, $(1,2)$, and $(0,2)$. What are the coordinates of its centre of mass?

Professor PC Thomas Classes · Answer

The L-shape consists of 3 squares of mass 1 kg each. Their geometric centres are $(0.5, 0.5)$, $(1.5, 0.5)$, and $(0.5, 1.5)$. The x-coordinate of the CM is $X = \frac{1(0.5) + 1(1.5) + 1(0.5)}{1+1+1} = \frac{2.5}{3} = \frac{5}{6}	ext{ m}$. By symmetry, the y-coordinate is also $\frac{5}{6}	ext{ m}$.