Four particles of masses m, 2m, 3m and 4m are arranged at the corners of a parallelogram with each side equal to a and one of the angle between two adjacent sides is `60^(@)`. The parallelogram lies in the x-y plane with mass m at the origin and 4 m on the x-axis. The centre of mass of the arrangement will be located at

Options

A. `((sqrt(3))/(2)a,0.95a)`
B. `(0.95a,(sqrt(3))/(4)a)`
C. `((3a)/(4),(a)/(2))`
D. `((a)/(2),(3a)/(4))`

Answer

B

Explanation

`X_(CM)=(m_(1)x_(1)+m_(2)x_(2)+m_(3)x_(3)+m_(4)x_(4))/(m_(1)+m_(2)+m_(3)+m_(4))`
`((a)/(2),(sqrt(3)a)/(2))(a+(a)/(2),(sqrt(3)a)/(2))`

`=(0+2mxx(a)/(2)+3mxx(3a)/(2)+4mxxa)/(10m)`
`=(a+4.5a+4a)/(10)=(9.5a)/(10)`
`X_(CM)=0.95a`
`Y_(CM)=(m_(1)y_(1)+m_(2)y_(2)+m_(3)y_(3)+m_(4)y_(4))/(m_(1)+m_(2)+m_(3)+m_(4))`
`=(0+2mxx(sqrt(3)a)/(2)+3mxx(sqrt(3)a)/(2)+4mxx0)/(10m)`
`=(2.5sqrt(3)a)/(10)=(sqrt(3))/(4)a`
:. `r_(CM)=(0.95a, (sqrt(3))/(4)a)`