The coordinates of the centre of mass of a un | vedclass

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(A) We can divide the $L$-shaped plate into two rectangular parts:Part $1$: $A$ rectangle from $x=0$ to $x=1$ and $y=0$ to $y=2$. Its area is $A_1 = 1

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$\left(\frac{5}{6} \ m, \frac{5}{6} \ m\right)$

Vedclass · Answer

(A) We can divide the $L$-shaped plate into two rectangular parts:Part $1$: $A$ rectangle from $x=0$ to $x=1$ and $y=0$ to $y=2$. Its area is $A_1 = 1 	imes 2 = 2 \ m^2$. Its centre of mass is at $(x_1, y_1) = (0.5, 1)$.Part $2$: $A$ rectangle from $x=1$ to $x=2$ and $y=0$ to $y=1$. Its area is $A_2 = 1 	imes 1 = 1 \ m^2$. Its centre of mass is at $(x_2, y_2) = (1.5, 0.5)$.Since the plate is uniform,the mass is proportional to the area. Total area $A = A_1 + A_2 = 3 \ m^2$.The $x$-coordinate of the centre of mass is $X_{cm} = \frac{A_1 x_1 + A_2 x_2}{A_1 + A_2} = \frac{2(0.5) + 1(1.5)}{3} = \frac{1 + 1.5}{3} = \frac{2.5}{3} = \frac{5}{6} \ m$.The $y$-coordinate of the centre of mass is $Y_{cm} = \frac{A_1 y_1 + A_2 y_2}{A_1 + A_2} = \frac{2(1) + 1(0.5)}{3} = \frac{2 + 0.5}{3} = \frac{2.5}{3} = \frac{5}{6} \ m$.Thus,the coordinates of the centre of mass are $\left(\frac{5}{6} \ m, \frac{5}{6} \ might)$.

The coordinates of the centre of mass of a uniform $L$-shaped plate of mass $3 \ kg$ shown in the figure is:

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