Four bodies of masses 2,kg, 3,kg, 5,kg and 8, | vedclass

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Question

(A) The coordinates of the corners of the square based on the figure are:$(0,0)$ for $2\,kg$,$(2,0)$ for $3\,kg$,$(2,2)$ for $5\,kg$,and $(0,2)$ for $

Vedclass · Accepted Answer

$\left( \frac{8}{9}, \frac{13}{9} \right)$

Vedclass · Answer

(A) The coordinates of the corners of the square based on the figure are:$(0,0)$ for $2\,kg$,$(2,0)$ for $3\,kg$,$(2,2)$ for $5\,kg$,and $(0,2)$ for $8\,kg$.The $x$-coordinate of the centre of mass is given by:$X_{CM} = \frac{m_1 x_1 + m_2 x_2 + m_3 x_3 + m_4 x_4}{m_1 + m_2 + m_3 + m_4}$$X_{CM} = \frac{2 	imes 0 + 3 	imes 2 + 5 	imes 2 + 8 	imes 0}{2 + 3 + 5 + 8} = \frac{0 + 6 + 10 + 0}{18} = \frac{16}{18} = \frac{8}{9}\,m$The $y$-coordinate of the centre of mass is given by:$Y_{CM} = \frac{m_1 y_1 + m_2 y_2 + m_3 y_3 + m_4 y_4}{m_1 + m_2 + m_3 + m_4}$$Y_{CM} = \frac{2 	imes 0 + 3 	imes 0 + 5 	imes 2 + 8 	imes 2}{2 + 3 + 5 + 8} = \frac{0 + 0 + 10 + 16}{18} = \frac{26}{18} = \frac{13}{9}\,m$Therefore,the coordinates of the centre of mass are $\left( \frac{8}{9}, \frac{13}{9} ight)$.

Four bodies of masses $2\,kg, 3\,kg, 5\,kg$ and $8\,kg$ are placed at the four corners of a square of side $2\,m$ as shown in the figure. The position of the centre of mass $(CM)$ is:

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