The centre of mass of a triangle shown in the | vedclass

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Question

(C) For a uniform triangular lamina,the centre of mass is located at the centroid of the triangle. If the vertices of the triangle are at $(x_1, y_1)$

Vedclass · Accepted Answer

$x = \frac{b}{3}, y = \frac{h}{3}$

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(C) For a uniform triangular lamina,the centre of mass is located at the centroid of the triangle. If the vertices of the triangle are at $(x_1, y_1)$,$(x_2, y_2)$,and $(x_3, y_3)$,the coordinates of the centroid $(x_{cm}, y_{cm})$ are given by: $x_{cm} = \frac{x_1 + x_2 + x_3}{3}$ and $y_{cm} = \frac{y_1 + y_2 + y_3}{3}$. From the figure,the vertices are $(0, 0)$,$(b, 0)$,and $(0, h)$. Substituting these values: $x_{cm} = \frac{0 + b + 0}{3} = \frac{b}{3}$ $y_{cm} = \frac{0 + 0 + h}{3} = \frac{h}{3}$ Thus,the coordinates of the centre of mass are $(\frac{b}{3}, \frac{h}{3})$.

The centre of mass of a triangle shown in the figure has coordinates

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