Three masses 2m, 4m and 6m are lying on peripery of a circle P, at points A, B, C respectively as shown in figure. Find the coordinate of centre of mass of system.

Options

A. `((a)/(3), (a)/(2))`
B. `((a)/(3), (a)/(2 sqrt3))`
C. `((a)/(2 sqrt3), (a)/(3))`
D. `((a)/(2 sqrt3), (a)/(2 sqrt3))`

Answer

B

Explanation

`2R cos 30^(@) = a`
`R = (a)/(sqrt3)`
So, `y = 2R sin 30^(@) = (a)/(sqrt3)`
`(bar(r )_(COM) = 2 m (0 hat(i)) + 4 m (a hat(i) + 0 hat(j)) + 6 m (0 hat(i) + (a)/(sqrt3) hat(j)))/(2m + 4m + 6m)`