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 as 60^(@) The parallelogram lies in the x-y plane with mass m at the origin and 4m on the r-axis. The centre of mass of the arrangement will be located at

Four particles of masses m, 2m, 3m and 4m are arranged at the corners

1.	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 as 60^(@) The parallelogram lies in the x-y plane with mass m at the origin and 4m on the r-axis. The centre of mass of the arrangement will be located at
Answer» `((SQRT3)/(2) a , 0.95 a)` `(0.95 a , (sqrt3)/(4) a)` `((3A)/(4) , (a)/(2))` `((a)/(2) , (3a)/(4))` Solution : `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))` `= ((m xx 0) + (2m xx (a)/(2)) + (3m xx (3a)/(2)) + (4M xx a))/(m+ 2m + 3m + 4m)` `= (ma + 4.5 ma + 4MA)/(10 m) = (9.5 ma)/(10m) = 0.95` a `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))` `(( m xx 0) + (2m xx (a sqrt3)/(2)) + (3m xx (a sqrt3)/(2)) 4 (4m xx0))/(m + 2m + 3m + 4m)` `= (sqrt3 am + sqrt3 xx 1.5 ma)/(10 m) = (2.5 sqrt3 am)/(10 m) = (sqrt3a)/(4)` `therefore` Centre of MASS is at `(0.95a , (sqrt3a)/(4))`