Find out the centre of mass of a system of these particles of 1 kg, 2 kg and 3 kg respectively kept at the vertices of an equilateral triangle of side 1 m as shown.

Explanation

`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)`