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

Find the position of centre of mass of the system of 3 objects of mass

1.	Find the position of centre of mass of the system of 3 objects of masses 1 kg, 2kg and 3 kg located at the corner of an equilateral triangle of side 1 m. Take 1 kg mass object at the origin and 2kg along x-axis.
Answer» Solution : `X_(CM)=(m_(1)x_(1)+m_(2)x_(2)+m_(3)x_(3))/(m_(1)+m_(2)+m_(3))` `rArr X_(cm)=(1xx0+2xx1+3xx(1)/(2))/(1+2+3)rArr X_(cm)=(7)/(12)m` `Y_(cm)=(m_(1)y_(1)+m_(2)y_(2)+m_(3)y_(3))/(m_(1)+m_(2)+m_(3))` `rArr Y_(cm)=(1xx0+2xx0+3xx(sqrt(3))/(2))/(1+2+3)rArr Y_(cm)=(sqrt(3))/(4)m` `THEREFORE` Co-ordinates of CENTRE of mass `(x_(cm), y_(cm))` `=((7)/(12)m, (sqrt(3))/(4)m)`