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The ratio of the radii of gyration of a ...

The ratio of the radii of gyration of a circular disc and a circular ring of the same radii about a tangential axis perpendicular to plane of disc or ring is

A

`1:2`

B

`2:3`

C

`3:4`

D

`sqrt5:sqrt6`

Text Solution

Verified by Experts

The correct Answer is:
D
`I_("Disc")=(5)/(4)MR^(2)=MK_(1)^(2)" "thereforeK_(1)=(sqrt5)/(2)R`
`I_("Ring")=(3)/(2)MR^(2)=MK_(2)^(2)" "therefore K_(2)=sqrt((3)/(2))R`
`therefore" "(K_(1))/(K_(2))=sqrt((5)/(6))`
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