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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.
1078566_f4ba16f4522f4cdd9fbfc7dc22c7fb18.png


Solution

 A=1k.g
B=2k.g
C=3k.g
D=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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