Point masses 1g, 2g, 4g and 3g are situated at the points A, B, C and D with .....?

position vectors i + j, -9i + 2j, 2i + 3j, and 5i - 3j, respectively. Find the position vector of the centre of mass for these four particles.





Any help is greatly appreciated.

Point masses 1g, 2g, 4g and 3g are situated at the points A, B, C and D with .....?
The moment of each particle about the x axis is its y co-ordinate multiplied by its mass.





Similarly, the moment of each particle about the y axis is its x co-ordinate multiplied by its mass.





The total moments about each axis must equal the moment about the same axis of a mass (1 + 2 + 4 + 3)g = 10g at the centre of mass.





For the x axis the moment is


(1 * 1 + 2 * 2 + 4 * 3 + 3 * (- 3))g


= 8g





For the y axis, it is:


(1 * 1 + 2 * (- 9) + 4 * 2 + 3 * 5)g


= 6g





For the centre of mass:


10gy = 8g


10gx = 6g


(x, y) = (0.6, 0.8).


The position vector is 0.6i + 0.8j.