If a solid sphere of mass 5kg and a disc of mass 4kg have the same...

Moment of inertia of the solid sphere about any diameter is given by, $\dfrac{2{m}_{1}{R}^{2}}{5}$.

Using parallel axis theorem, we get

${I}_{\text{solid sphere}} = \dfrac{2}{5}{m}_{1}{R}^{2} + {m}_{1}{R}^{2} = \dfrac{7}{5}{m}_{1}{R}^{2}$

$= \dfrac{7}{5} \times 5{R}^{2}$

$= 7{R}^{2}$

Moment of inertia of the disc about the diameter is given by, $\dfrac{{m}_{2}{R}^{2}}{4}$.

Now using parallel axis theorem, we get

${I}_{\text{disc}} = \dfrac{{m}_{2}{R}^{2}}{4} + {m}_{2}{R}^{2} = \dfrac{5}{4}{m}_{2}{R}^{2}$

$= \dfrac{5}{4} \times 4{R}^{2}$

$= 5{R}^{2}$

Therefore,$\dfrac{{I}_{\text{disc}}}{{I}_{\text{soild sphere}}} = \dfrac{5}{7}$

Thus, $x = 5$.