Three thin uniform rods made of same material are joined as shown. Locate x coordinate of COM.

Options

A. L/2
B. L/3
C. L/4
D. L

Answer

A

Explanation

Here , mass is distributed on length .Since density is same, hence `mass prop length`.
Rod `(1) mass m_(1) prop L rArr m_(1) = kL = m`
Rod `(2) m_(2) prop sqrt(2) L rArr m_(2) = k sqrt(2 L) = sqrt(2) m`
Rod `(3) m_(3) = m`
`{:(, x,y),(m_(1) = m ,(L)/(2) , 0) , (m_(2) = sqrt(2) m , (sqrt(2)L)/(2) cos 45^(@) = (L)/(2) ,(sqrt(2)L)/(L) sin 45^(@) = (L)/(2)),(m_(3) = m ,(L)/(2) ,(L)):}`
`x_(c.m.) = (m xx (L)/(2) + sqrt(2) m xx (L)/(2) + m xx (L)/(2))/(m + sqrt(2)m + m) = (L)/(2)`
`y_(c.m.) = (m xx 0 + sqrt(2) m (L)/(2) + mL)/(m + sqrt(2) m + m) = (L)/(2)`