Three particles of masses 100g, 150g and 200g are 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, 3sqrt(3))`
B. `(1/(3sqrt(3)), 5/13)`
C. `(5/18, 1/(3sqrt(3)))`
D. `(18/5, 1/sqrt(13))`

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 sqrt(3))`. Let the masses 100 g, 150 g and 200 g is located at O, A and B. Then,
`x=(m_(1)x_(1)+m_(2)x_(2)+m_(3)x_(3))/(m_(1)+m_(2)+m_(3))`
`x=([100(0)+150(0.5)+200(0.25)]g)/((100+150+200)g) rArr 5/18m`
`y=([100(0)+150(0)+200(0.25sqrt(3))])/(450)=(50sqrt(3))/(450)=sqrt(3)/9m=1/(3sqrt(3))m`