Question

A rectangular slab $ABCD$ have dimensions $a\times 2a$ as shown in figure. Match the following two columns

Answer 1

(a) MI about axis-1: $I_{axis-1}=I_{axis-2}+m{a}^2$ using parallel axis theorem
$\therefore I_{axis-1}=\frac{m}{12}(2a{)}^2+m{a}^2=\frac{4m{a}^2}{3}=m{k}^2$
$\Rightarrow k=\frac{2a}{\sqrt{3}}$
(b) $I_{axis-2}=\frac{m}{12}(2a{)}^2=\frac{m{a}^2}{3}=m{k}^2$
$\Rightarrow k=\frac{a}{\sqrt{3}}$
(c) $I_{axis-3}=\frac{m}{12}(a{)}^2+m(\frac{a}{2}{)}^2=m{k}^2$
$\Rightarrow k=\frac{a}{\sqrt{3}}$
(d) $I_{axis-4}=\frac{m}{12}(a{)}^2=m{k}^2$
$\Rightarrow k=\frac{a}{\sqrt{12}}$