Particles of masses 3 kg, 4 kg, 5 kg nd 2 kg are placed at points `A(3,2), B(-2,2), C(-2,-3)` and `D(1,-2)` respectively of a co-ordinate system. The centre of mass of the system is at

Options

A. `(-(1)/(2),-(1)/(2))`
B. `(-(1)/(2),-(5)/(14))`
C. `(0,-(1)/(2))`
D. (0,0)

Answer

B

Explanation

(i) `x = (m_(1)n_(1)+m_(2)x_(2)+m_(2)x_(3)+m_(4)x_(4))/(m_(1)+m_(2)+m_(3)+m_(4))=(-7)/(14)=(-1)/(2)`
(ii) `y=(m_(1)y_(1)+m_(2)y_(2)+m_(3)y_(3)+m_(4)y_(4))/(m_(1)+m_(2)+m_(3)+m_(4))=(-5)/(14)`
(x,y) of centre of mass `=((-1)/(2), (-5)/(14))`.