Physics - Center of Mass Question with Solution | TestHub

A thin rod of length ' $L$ ' is lying along the $x$-axis with its ends at $x=0$ and $x=L$. Its linear density (mass/length) varies with $x$ ask ${\left(\frac{x}{L}\right)}^n$, where $n$ can be zero or any positive number. If the position $x_{\mathrm{CM}}$ of the centre of mass of the rod is plotted against ' $n$ ', which of the following graphs best approximates the dependence of $x_{\mathrm{CM}}$ on $n$ ?