Physics - Rotation Question with Solution | TestHub

A nonuniform rod $OM$  of length $\mathrm{l}$ has linear mass density that varies with the distance $x$ from left end of the rod according to $\lambda ={\lambda }_0\left(\frac{x^3}{L^3}\right)$; Where ${\lambda }_0$  is constant, is kept along $x$-axis and is rotating about an axis $AB$, which is perpendicular to the rod as shown in the figure. What is the value of $x$  so that moment of inertia of rod about axis $A\mathrm{B }\left({\text{I}}_{AB}\right)$  is minimum?