Two bodies with moment of inertia ${\text{I}}_1\text{and}{\text{I}}_2\left({\text{I}}_2>{\text{I}}_1\right)$ are rotating with same angular momentum. If ${\text{K}}_1\text{and}{\text{K}}_2$ are their kinetic energies, then

$I_1{\omega }_1=I_2{\omega }_2$ $\left(\because \text{Given}{I}_2>I_1\right)$ $\therefore \frac{I_2}{I_1}>1$

$\frac{I_2}{I_1}=\frac{{\omega }_1}{{\omega }_2}$

$\Rightarrow \frac{{\omega }_1}{{\omega }_2}>1$

$\Rightarrow {\omega }_1>{\omega }_2$

We Know That Rotational Kinetic Energy

$K=\frac{1}{2}I{\omega }^2$

${\text{K}}_{\text{1}}=\frac{1}{2}{I}_1{\omega }_1^2$

${\text{K}}_{\text{2}}=\frac{1}{2}{I}_2{\omega }_2^2$

${\text{K}}_{\text{1}}=\left(\frac{1}{2}{I}_1{\omega }_1\right){\omega }_1$

${\text{K}}_{\text{2}}=\left(\frac{1}{2}{I}_2{\omega }_2\right){\omega }_2$

${\omega }_1>{\omega }_2$

$\Rightarrow {\text{K}}_{\text{1}}>{\text{K}}_{\text{2}}$

$\Rightarrow {\text{K}}_{\text{2}}<{\text{K}}_{\text{1}}$