Three particles of masses 100 g, 150 g and 200.gare placed at the vertices of an equilateral triangle. Each side of the triangle is 0.5 m long. The centre of mass of the three particle is

Options

A. `(18/5,3sqrt3)`
B. `(1/(3sqrt3),5/13)`
C. `(5/18,1/(3sqrt3))`
D. `(18/5,1/(sqrt13))`

Answer

C

Explanation

With the x and y-axis chosen as the coordinates of points o A and B forming the equilateral triangle are respectively (0,0), (0.5,0), (0.25, 0.25 `sqrt3`). Let the masses 100 g, 150 g and 200 g is located at 0, A and B. Then,
`x=(m_1x_1 + m_2x_2 +m_3x_3)/(m_1+m_2+m_3)`
`x=([100(0) +150(0.5)+200(0.25)]g)/((100+150+200)g)implies5/18m`
`y=([100(0)+150(0) +200(0.253)])/450 = (50sqrt3)/450=sqrt3/9m =1/(3sqrt3)m`