Three bodies each of mass 1 ,kg are situated | vedclass

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(D) Let the coordinates of the three masses be $(x_1, y_1) = (0, 0)$,$(x_2, y_2) = (1, 0)$,and $(x_3, y_3) = (0.5, \frac{\sqrt{3}}{2})$.All masses are

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$\left(\frac{1}{2}, \frac{1}{2 \sqrt{3}}\right)$

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(D) Let the coordinates of the three masses be $(x_1, y_1) = (0, 0)$,$(x_2, y_2) = (1, 0)$,and $(x_3, y_3) = (0.5, \frac{\sqrt{3}}{2})$.All masses are equal,$m_1 = m_2 = m_3 = 1 \,kg$.The $x$-coordinate of the centre of mass is given by:$X_{cm} = \frac{m_1 x_1 + m_2 x_2 + m_3 x_3}{m_1 + m_2 + m_3} = \frac{1(0) + 1(1) + 1(0.5)}{1 + 1 + 1} = \frac{1.5}{3} = \frac{1}{2} \,m$.The $y$-coordinate of the centre of mass is given by:$Y_{cm} = \frac{m_1 y_1 + m_2 y_2 + m_3 y_3}{m_1 + m_2 + m_3} = \frac{1(0) + 1(0) + 1(\frac{\sqrt{3}}{2})}{1 + 1 + 1} = \frac{\frac{\sqrt{3}}{2}}{3} = \frac{\sqrt{3}}{6} = \frac{1}{2 \sqrt{3}} \,m$.Thus,the coordinates of the centre of mass are $\left(\frac{1}{2}, \frac{1}{2 \sqrt{3}}\right)$.

Three bodies each of mass $1 \,kg$ are situated at the vertices of an equilateral triangle of side $1 \,m$. The $x y$-coordinates of the centre of mass of the system are:

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