Question

Moment of inertia of a uniform rod of length $L$ and mass $M$, about an axis passing through $L/4$ from one end and perpendicular to its length is

• A. $\frac{7}{36}{ML}^2$
• B. $\frac{{ML}^2}{12}$
• C. $\frac{7}{48}{ML}^2$
• D. $\frac{11}{48}{ML}^2$

Answer 1

The correct option is C $\frac{7}{48}{ML}^2$

Moment of inertia through centre of rod=$\frac{M{l}^2}{12}$

Moment of inertia through a point at a distance of $\frac{l}{4}$ from an end is I=$\frac{M{l}^2}{12}+\frac{M{l}^2}{16}=\frac{7M{l}^2}{48}$