Question

A uniform rod of length $l$ is rotated about its end and it has a moment of inertia $\alpha kg{m}^2$. What is the moment of inertia of a rod about a point $\frac{l}{4}$ away from the center?

• A. $\frac{7}{16}\alpha$
• B. $\frac{5}{18}\alpha$
• C. $\frac{3}{12}\alpha$
• D. $\frac{4}{13}\alpha$

Answer 1

The correct option is A $\frac{7}{16}\alpha$

$I_{A{A}^1}=\frac{M{l}^2}{3}=\alpha$
$I_{B{B}^1}=\frac{M{l}^2}{12}+\frac{M{l}^2}{16}$
$=\frac{4M{l}^2}{48}+\frac{3M{l}^2}{48}=\frac{7M{l}^2}{48}$
$=\frac{7}{16}\left(\frac{M{l}^2}{3}\right)=\frac{7}{16}\alpha$