Three rings, each of mass `m` and radius `r`, are so placed that they touch each other. Find the moment of inertia about the axis as shown in Fig.

Options

A. `sqrt(6/5)r`
B. `sqrt(5/6)r`
C. `sqrt(6/7)r`
D. `sqrt(7/6)r`

Answer

D

Explanation

`I=I_(1)+I_(2)+I_(3)`
`I_(1)=I_(2)=3/2 mr^(2)`
`I_(3)=(mr^(2))/2`
`:. I=I_(1)+I_(2)+I_(3)=7/2 mr^(2)`
moment of inertia=`3 mk^(4)` where k is radius of gyration
`3 mk^(2)=7/2 mr^(2)`
`rArr k=sqrt(7/6)r`