Three point masses `m_(1) = 2Kg, m_(2) = 4kg and m_(3)= 6kg` are kept at the three corners of an equilateral triangle of side 1 m. Find the locationo of their center of mass.

Explanation

Assume `m_(1)` to be at the origin and x-axis along the line joining `m_(1)` to `m_(2)` as shown in figure.

From the figure it is clear that the x-y co-ordinates of `m_(1)` is `(x_(1),y_(1))=(0, 0)`, that of `m_(2)` is `(x_(2), y_(2))=(1,0)` and that of `m_(3)` is `(x_(3), y_(3))=((1)/(2), (sqrt(3))/(2))`
`x_(CM)=(2xx0+4xx1+6xx(1)/(2))/(2+4+6)=(7)/(12)m`
`y_(CM)=(2xx0+4xx0+6xx(sqrt(3))/(2))/(2+4+6)=(3sqrt(3))/(12)=(sqrt(3))/(4)m`
`therefore` CM is at `((7)/(12), (sqrt(3))/(4))`