Question

There are four rods $A,B,C$ and $D$ of same length $l$ but different linear mass density $d,2d,3d$ and $4d$ respectively. These are joined to form a square frame with sides $C$ and $D$ along x and y axis of coordinate axes respectively. Find coordinate of centre of mass of structure.

Answer 1

the four rods m 2m 3m 4m

$X_{cm}=\frac{m\left(\frac{l}{2}\right)+2m\left(l\right)+3m\left(\frac{l}{2}\right)+4m\left(0\right)}{m+2m+3m+4m}$

$\frac{40ml}{10m}=\frac{2l}{5}$

$Y_{cm}=\frac{m\left(l\right)+2m\left(\frac{l}{2}\right)+3m\left(0\right)+4m\left(\frac{l}{2}\right)}{m+2m+3m+4m}$

$\frac{40ml}{10m}=\frac{2l}{5}$

$\left(X_{cm}{Y}_{cm}\right)=\frac{2l}{5},\frac{2l}{5}$