Find the centre of mass of three particles at the vertices of an equilateral triangle .The masses of the particles are 100 gram, 150 gram and 200 gram respectively .Each side of the equilateral triangle is 0.5 m long.

Explanation

Length of side =0.5 m
mass `m_(1)=100` g
`m_(2)=150g and m_(3)=150` g
distances `x_(1)=0,y_(1)=0`,
`x_(2)=0.5,y_(2)=0`
`x_(3)=0.25,y_(3)=0.25sqrt(3)`

Centre of mass `X_(cm)=(m_(1)x_(1)+m_(2)x_(2)+m_(3)x_(3))/(m_(1)+m_(2)+m_(3))`
`=(0+150xx(0.5)+200xx0.25)/(100+150+200)`
`X_(c.m)=(75+50)/(450)=(125)/(450)=(5)/(18)m`
`Y_(c.m)=(m_(1)y_(1)=m_(2)y_(2)+m_(3)y_(3))/(m_(1)+m_(2)+m_(3))`
`=(100+0+150xx0+200xx0.25sqrt(3))/(450)`
`(50sqrt(3))/(450)=(sqrt(3))/(9)=(1)/(3sqrt(3))m`.