A wire of uniform cross-section is bend in the shape shown in figure. The co-ordinate of the centre of mass of each side are shown in (figure). The co-ordinates of the centre of mass of the system are.
.

Options

A. `((15 l)/(14), (6l)/(7))`
B. `((15 l)/(14),l)`
C. `(l, (l)/(2))`
D. `(l, l)`

Answer

A

Explanation

(a) `X_(cm) = (m xx 0 + ml + m xx 2l + (m)/(2)(3 l)/(2))/(3.5 m)`
`rArr X_(cm) = (15 ml)/(4 xx (7)/(2) m) =(15 l)/(14)`
`Y_(cm) = (m xx 0 + ml + ml + (m)/(2) 2l)/(7/(2)m) `
`rArr Y_(cm) = (3 ml)/((7 m)/(2)) = (6l)/(7)`.