Physics - Rotation Question with Solution | TestHub

The linear mass density of a thin rod$\mathrm{AB}$of length$\mathrm{L}$varies from$\mathrm{A}$to$\mathrm{B}$as$\mathrm{\lambda }\left(\mathrm{x}\right)={\mathrm{\lambda }}_0\left(1+\frac{\mathrm{x}}{\mathrm{L}}\right)$, where$\mathrm{x}$is the distance from$\mathrm{A}$. If$\mathrm{M}$is the mass of the rod then its moment of inertia about an axis passing through$\mathrm{A}$and perpendicular to the rod :