Find the position of centre of mass of the system of 3 objects of masses 1 kg, 2 kg and 3 kg located at the comers of an equilateral triangle of side 1 m. Take 1 kg mass object at the origin and 2 kg is along x-axis.

Explanation

Mass of the first object `m_(1) = 1kg` , Mass of the second object, `m_(2) = 2kg`
Mass of the third object, `m_(3) = 3kg`, Co- ordinates of first object, `(x_(1),y_(1)) =(0,0)`
`x_(cm) = (m_(1)x_(1) + m_(2)x_(2) + m_(3)x_(3))/(m_(1) + m_(2) + m_(3))`
`rArr x_(cm) (1 xx 0 + 2 xx 1 + 3 xx 1/2)/(1+2+3) rArr x_(cm) = 7/12 cm`
`Y_(cm) =(m_(1)y_(1) + m_(2)y_(2) + m_(3)y_(3))/(m_(1) + m_(2) + m_(3))`
`rArr Y_(cm) = (1 xx 0 + 2 xx 0 + 3 xx sqrt(3)/2)/(1+2+3) rArr Y_(cm) = sqrt(3)/4` m
Co- ordinates of centre of mass `(x_(cm), y_(cm)) = (7/12m, sqrt(3)/4 m)`