Three particles of masses 1 g, 2g, and 3g are placed at the vertices of an equilateral triangle of side 1 m. Locate the centre of mass of the system.

Explanation

Suppose, the triangle lies on the XY- plane. The particle of mass `m_(1)` = 1 g is placed at the origin O which is one of the vertices of the triangle. `m_(1)` and `m_(2)` lie on the x-axis. Let the coordinates of the centre of mass of the system be `(x_("cm"), y_("cm")`).
`:." " x_("cm")=(m_(1)x_(1)+m_(2)x_(2)+m_(3)x_(3))/(m_(1)+m_(2)+m_(3))=(1xx0+2xx1+3xx(1)/(2))/(1+2+3) = (7)/(12) m`
and `y_("cm")=(m_(1)y_(1)+m_(2)y_(2)+m_(3)y_(3))/(m_(1)+m_(2)+m_(3))=(1xx0+2xx0+3xx(sqrt(3))/(2))/(1+2+3)=(sqrt(3))/(4)m`
`:.` The coordinates of the centre of mass are `((7)/(12),(sqrt(3))/4)`.