$\Rightarrow$ angular momentum conservation
$\mathrm{I}_{1} \mathrm{\omega}_{1}=\mathrm{I}_{2} \mathrm{\omega}_{2}$
Let $\mathrm{\omega}_{1}=\mathrm{\omega}_{0}$
$\mathrm{mR}^{2} \mathrm{\omega}_{0}=\frac{\mathrm{mR}^{2}}{\mathrm{n}^{2}} \mathrm{\omega}^{2}$
$\Rightarrow \mathrm{\omega}_{2}=\mathrm{\omega}_{0} \eta^{2}$
$=\left(\mathrm{k}_{0}=\frac{1}{2} \mathrm{I}_{1} \mathrm{\omega}^{2}\right)$
$\mathrm{k}_{0}=\frac{1}{2} \times\left(\mathrm{mR}_{0}^{2}\right) \mathrm{\omega}_{0}^{2}=\frac{\mathrm{m} \mathrm{R}_{0}^{2} \mathrm{\omega}_{0}^{2}}{2}$
Here change in $\mathrm{K} . \mathrm{E} .=(\mathrm{WD})$
$\mathrm{k}_{f}=\frac{1}{2} \mathrm{I}_{2} \mathrm{\omega}_{2}^{2}=\frac{1}{2} \times\left(\frac{\mathrm{mR}^{2}}{\eta^{2}}\right) \times \mathrm{\omega}_{0}^{2} \eta^{4}$
$=\left(\frac{1}{2} \mathrm{mR}^{2} \mathrm{\omega}_{0}^{2}\right) \eta^{2}$
$\mathrm{WD}=\mathrm{k}_{\mathrm{f}}-\mathrm{k}_{\mathrm{i}}=\frac{1}{2} \mathrm{mR}^{2} \mathrm{\omega}_{0}^{2}\left(\eta^{2}-1\right)$
$=k_{0}\left(\eta^{2}-1\right)$
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