The density of a non-uniform rod of length 1 m is given by $\rho \left(x\right)=a(1+b{x}^2)$  where a and b are constants and  $0\le x\le 1$. The centre of mass of the rod will be at

Density is given as  $p\left(x\right)=a(1+b{x}^2)$  where a and b are constants and  $0\le x\le 1$
Let  $b\to 0,$ in this cases $p\left(x\right)=a=$ constant Hence, centre of mass will be at $x=0.5m.$ (middle of the rod)