Question

# Four point masses are placed at the corners of a square of side 2 m as shown in the figure. Find the centre of mass of the system w.r.t. the centre of square.

Solution

## A=1k.gB=2k.gC=3k.gD=4k.g$$X_cm=\dfrac{m_1\times x_1+m_2\times x_2+m_3\times x_3+m_4\times x_4}{m_1+m_2+m_3+m_4}$$$$X_cm=\dfrac{(1\times 1)+(2\times 1)+(3\times -1)+(4\times -1)}{1+2+3+4}$$$$X_cm=\dfrac{1+2-3-4}{10}=\dfrac{-4}{10}$$$$X_cm= -0.4$$$$Y_cm=\dfrac{m_1\times y_1+m_2\times y_2+m_3\times y_3+m_4\times y_4}{m_1+m_2+m_3+m_4}$$$$Y_cm=\dfrac{(1\times 1)+(-1\times 2)+(-1\times 3)+(4\times 1)}{1+2+3+4}$$$$Y_cm=\dfrac{1-2-3+4}{10}=\frac{0}{10}$$$$Y_cm=0$$The coordinate of center of mass (-0.4,0)Physics

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