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

Explanation

Mass at A = 100g, Coordinates = 0,0
Mass at B = 150 g, Coordinates = (0.5, 0).
Mass at C = 200g, Coordinates (0.25, 0.25 `sqrt3` )
Coordinates `X_(cm)`
`X_(CM) = (m_A x_A + m_B x_B + m_C x_C)/(m_A + m_B + m_C)`

`= ((100 xx 0 ) + (150 xx 0.5) +(1200 xx 0.25))/(100 + 150 + 200)`
` (75+50)/(450) = 125/450 = 5/18 m`
`Y_(CM) = ((m_A y_A + m_By_B + m_C y_C))/(m_A + m_B + m_C)`
` = ((100xx0)+(150xx0) +(200xx0.25sqrt3))/(100+150+200)`
`= (50sqrt3)/(450) = (sqrt3)/(9) = (1)/(3 sqrt3)m`