The moment if inertia of thin rod of mass. $M$ and length L about an axis perpendicular to the rod a

Question

The moment if inertia of thin rod of mass. $M$ and length L about an axis perpendicular to the rod at distance $\mathrm{L} / 4$ from one end is\

Professor PC Thomas Classes · Answer

D) Moment of inertia of uniform $\operatorname{rod}=\frac{M L^{2}}{12}$ Now at a distance $\mathrm{L} / 4$, the moment of inertia will be\ $\frac{M L^{2}}{12}+M\left(\frac{L}{4}ight)^{2}=\frac{M L^{2}}{12}+\frac{M L^{2}}{16}=\frac{M L^{2}}{4}\left(\frac{1}{3}+\frac{1}{4}ight)$\ $=\frac{\mathrm{ML}^{2}}{4}\left(\frac{7}{12}ight)=\frac{7 \mathrm{ML}^{2}}{48}$