Two thin uniform rings made of same material and of radii Rand 4R are joined as shown. The mass of smaller ring is m. Find the moment of inertia of the system about an axis passing through the center of mass of bigger ring and perpendicular to the plane:

Options

A. `85 mR ^(2)`
B. `90 mR ^(2)`
C. `70 mR ^(2)`
D. `35 mR ^(2)`

Answer

B

Explanation

`I = I _("larger") + I _("smaller")`
`I = 4 M (4 R) ^(2)`
`+ [ MR^(2) + M ( 5 R) ^(2) ] = 90 MR ^(2)`