Question

Two rings of radius R and nR made of same material have the ratio of moment of inertia about an axis passing through center is `1:8`. The value of n is
A. 2
B. `2sqrt(2)`
C. 4
D. `1/2`

Answer 1

a)
Ratio of moment of the rings
`I_(1)/I_(2) = (M_(1)/M_(2))(R_(1)/R_(2))^(2) = (lambdaL_(1)/(lambdaL_(2))^(2)(R_(1)/R_(2))^(2)`
`(2piR)/(2pinR)(R/(nR)^(2)` [`lambda` = linear density of wire = constant]
`rArr L_(1)/L_(2) = 1/n^(3) = 1/8`
`therefore` `n^(3) = 8`
`rArr n=2`