$$dI = (dm)r^{2}$$ $$\Rightarrow (\sigma dA)r^{2}$$ $$\Rightarrow (\frac{\sigma_{0}}{r})r^{2}$$ $$\Rightarrow (\sigma _{0}2\Pi dr)r^{2}dr$$

I = $$\int dI = \int_{a}^{b}\sigma _{0}2\Pi dr)r^{2}dr$$ $$\Rightarrow \sigma _{0}2\Pi(\frac{b^{3} – a^{3}}{3})$$

m = $$\int dm = \int \sigma dA$$ $$\Rightarrow \sigma _{0}2\Pi\int_{a}^{b}dr$$

m = $$\sigma _{0}2\Pi(b-a)$$

k = $$\sqrt{\frac{I}{m}} = \sqrt{\frac{(b^{3} – a^{3})}{3(b -a)}}$$ $$\Rightarrow \sqrt{(\frac{a^{3} + b^{3} + ab}{3})}$$

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