Three rods of the same mass are placed as shown in the figure. Calculate the coordinates of the centre of mass of the system.

Options

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

Answer

A

Explanation

Ans.(1)

Centre of Mass of rod `OA` is at `((a)/(2),0)`
Centre of Mass of rod `OB` is `(0,(a)/(2))`
Centre of Mass of rod `AB` is `((a)/(2),(a)/(2))`
For system `X_(cm)=(mxx(a)/(2)+mxx0+mxx(a)/(2))/(m+m+m)=(a)/(3)`
& `Y_(cm)=(mxx0+mxx(a)/(2)+mxx(a)/(2))/(m+m+m)=(a)/(3)`