A rod of length L has non-uniform linear mass density given by ρ(x)= a + b (x/L)^2, where a and b are constants and 0 ≤ x ≤ L. The value of x for the…

A rod of length L has non-uniform linear mass density given by $\displaystyle \rho(x)=\mathrm{a}+\mathrm{b}\left(\frac{x}{\mathrm{~L}}\right)^2$, where a and b are constants and $\displaystyle 0 \leq x \leq \mathrm{L}$. The value of $\displaystyle x$ for the centre of mass of the rod is at: