Four particles of masses m,2m, 3m ,4m are placed at the corners of a square of side 'a' as shown in the figure. Find out the co-ordinates of centre of mass.

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Solution

Let co-ordinates of center of mass is $M (x, y)$ .
$x = \frac{m_{1} x_{1} + m_{2} x_{2} + m_{3} x_{3} + m_{4} x_{4}}{m_{1} + m_{2} + m_{3} + m_{4}} = \frac{m \times 0 + (4 \times 0 + 3 \times a + 2 \times a) m}{m + 4 m + 3 m + 2 m} = \frac{5 a m}{10 m} = \frac{1}{2} a y = \frac{m \times 0 + 4 m \times a + 3 m \times a + 2 m \times 0}{10 m} = \frac{7 a m}{10 m} = \frac{7}{10} a M (\frac{1}{2} a, \frac{7}{10} a)$

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Four particles of masses m,2m, 3m ,4m are placed at the corners of a square of side 'a' as shown in the figure. Find out the co-ordinates of centre of mass.

Let co-ordinates of center of mass is M(x,y).x=m1x1+m2x2+m3x3+m4x4m1+m2+m3+m4=m×0+(4×0+3×a+2×a)mm+4m+3m+2m=5am10m=12ay=m×0+4m×a+3m×a+2m×010m=7am10m=710aM(12a,710a)