Answer:
[tex]\frac{I_{disc}}{I_{sphere}} = \frac{5}{8}[/tex]
Explanation:
As we know that the moment of inertia of the disc is given as
[tex]I_{disc} = \frac{1}{2}mR^2[/tex]
here we know that
[tex]mass = 2m[/tex]
[tex]radius = R[/tex]
[tex]I_{disc} = mR^2[/tex]
Now for sphere the moment of inertia is given as
[tex]I_{sphere} = \frac{2}{5}mR^2[/tex]
here we know that
[tex]mass = m[/tex]
[tex]radius = 2R[/tex]
[tex]I_{disc} = \frac{2}{5}m(2R)^2= \frac{8}{5}mR^2[/tex]
now the ratio of two moment of inertia is
[tex]\frac{I_{disc}}{I_{sphere}} = \frac{mR^2}{1.6mR^2}[/tex]
[tex]\frac{I_{disc}}{I_{sphere}} = \frac{5}{8}[/tex]
