Two identical rods each of mass `m` and length are connected as shown. Locate `c.m.`

Explanation

(a) This system is symmetrical about the `x`-axis . Hence we need to find `x_(c.m.)`. Here we will take coordinates of `c.m.` of rods.
`{:(,x - co o rd i n a t e),(Rod(1) m_(1) = m,0),(Rod(2) m_(2) = m ,(L)/(2)):}`
`x_(c.m.) = ( m xx 0 + m xx (L)/(2))/(m + m) = (m (L)/(2))/(2m) = (L)/(4)`
`y_(c.m.) = 0`
`c.m. -= ((L)/(4) , 0)`
(b) Symmetry about the `y`-axis:
`{:(,y - co ordi na te), (Rod (1) m_(1) = m , (L)/(2)),(Rod(2) m_(2) = m ,(L)):}`
`y_(c.m.) = (m xx (L)/(2) + m xx L)/(m + m) = (3L)/(4)`
(c ) Symmetry about the `y`-axis:
`{:(,y - co ordi na te), (Rod (1) m_(1) = m , (L)/(2) cos 60^(@) = (L)/(4)),(Rod(2) m_(2) = m ,(L)/(2) cos 60^(@) = (L)/(4)):}`
`y_(c.m.) = ( m xx (L)/(4) + m xx (L)/(4))/(m + m) = (L)/(4)`
(d) Not symmetrical about any axis
`{:(,,x ,y), (Rod (1) ,m_(1) = m , (L)/(2), 0),(Rod(2), m_(2) = m ,0 ,(L)/(2)):}`
`x_(c.m.) = (m xx (L)/(2) + m xx 0)/(m + m) = (L)/(4)`
`y_(c.m.) = ( m xx 0 + m xx (L)/(2))/(m + m) = (L)/(4)`
coordinates of `c.m. -= ((L)/(4) ,(L)/(4))`