Two uniform circular discs A and B of radii R and 4R with thicknesses x and x/4 respectively, rotate about their axes passing through their centres and perpendicular to their planes. If the M.I. of the first disc is `I_(A)` and that of the second disc is `I_(B)` then

Options

A. `I_(A)=I_(B)`
B. `I_(A) gt I_(B)`
C. `I_(B) gt I_(A)`
D. Data is insufficient

Answer

C

Explanation

For the disc A, `I_(A)=(1)/(2)M_(1)R^(2)`
But mass `M_(1)="volume "xx"density"=piR^(2)xrho`
`therefore I_(A)=(1)/(2)piR^(2)x rho(R^(2))" …(1)"`
and `I_(B)=(1)/(2)M_(2)R'^(2)`
`=(1)/(2)(pi.16R^(2))xx(x rho)/(4)xx16R^(2)" ...(2)"`
`therefore" "(I_(B))/(I_(A))=16xx(1)/(4)xx16=64`
`therefore I_(B) gt I_(A)`