Question

The radius of gyration of uniform disc of radius $r$, about an axis passing through $r/4$ from center of disc and perpendicular to plane of disc is

• A. $3r/4$
• B. $r/2$
• C. $r/3$
• D. $r/8$

Answer 1

The correct option is A $3r/4$


$I_{A{A}^{\prime }}=I_{CM}+m{d}^2$
$I_{A{A}^{\prime }}=\frac{m{r}^2}{2}+m(r/4{)}^2$
$I_{A{A}^{\prime }}=\frac{m{r}^2}{2}+\frac{m{r}^2}{16}=\frac{9m{r}^2}{16}$
$I_{A{A}^{\prime }}=m{k}^2=\frac{9m{r}^2}{16}$
$\Rightarrow k=\frac{3}{4}r$