A solid sphere and a solid cylinder of same mass and radius are...

Considering rotational axis as the diametrical axis for sphere and axis of cylinder. Then

${K}_{1}^{2} = \dfrac{2}{5}{R}^{2}$ and ${K}_{2}^{2} = \dfrac{1}{2}{R}^{2}$

$∴ \dfrac{{K}_{1}}{{K}_{2}} = \sqrt{\dfrac{2 / 5}{1 / 2}} = \sqrt{\dfrac{4}{5}}$

$⇒ \dfrac{{K}_{1}}{{K}_{2}} = \dfrac{2}{\sqrt{5}}$

Comparing it with the given value in the question,

$\dfrac{2}{\sqrt{5}} = \dfrac{2}{\sqrt{x}}$

$∴$ $x = 5$