The ratio of the radii of gyration of a circular disc to that of a circular ring, each of same mass and radius, around their respective axes is.

Options

A. `sqrt3:sqrt2`
B. `1:sqrt2`
C. `sqrt2:1`
D. `sqrt2:sqrt3`

Answer

B

Explanation

Radius of gyration is given by, `K=sqrt((l)/(M))`
For given, problem, `(K_("disc"))/(K_("ring"))=sqrt((l_("disc"))/(l_("ring")))" …(i)"`
`"But "l_("disc")=(1)/(2)MR^(2) and l_("ring")=MR^(2)" (about its axis)"`
where, R is the radius of both bodies.
Therefore, Eq. (i) becomes `(K_("disc"))/(K_("ring"))=sqrt(((1//2)MR^(2))/(MR^(2)))`
`=1:sqrt2`