Physics - Rotation Question with Solution | TestHub

Mass of the solid sphere, $M_s=5$ kg
Mass of the disc, $M_d=4$ kg
Let the radius of both the sphere and the disc be $R$.

The moment of inertia of a solid sphere about its tangent is obtained using the parallel axis theorem:
$I_s=I_{cm}+M_s{R}^2=\frac{2}{5}{M}_s{R}^2+M_s{R}^2=\frac{7}{5}{M}_s{R}^2$
Substituting $M_s=5$ kg:
$I_s=\frac{7}{5}\times 5\times R^2=7R^2$

The moment of inertia of a disc about a tangent in its plane is also obtained using the parallel axis theorem (shifting from the diameter):
$I_d=I_{diameter}+M_d{R}^2=\frac{1}{4}{M}_d{R}^2+M_d{R}^2=\frac{5}{4}{M}_d{R}^2$
Substituting $M_d=4$ kg:
$I_d=\frac{5}{4}\times 4\times R^2=5R^2$

The ratio of their moments of inertia is:
$\frac{I_s}{I_d}=\frac{7R^2}{5R^2}=\frac{7}{5}$

Comparing this with $x:y$, we get $x=7$ and $y=5$.

Answer: $7,5$