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. `sqrt(3) :sqrt(2)`
B. `1 :sqrt(2)`
C. `sqrt(2) :1`
D. `sqrt(2) :sqrt(3)`

Answer

B

Explanation

radius of gyration is given by `K = sqrt(I/M)` For given
problem `(K_("disc"))/(K_("ring") ) = sqrt((I_("disc"))/(M_("ring"))) .......(i)`
But `I_("disc")` (abut its axis ) ` = 1/2 MR^(2) and I_("ring")` (about tis axis ) = `MR^(2)` , where R is the radius of both bodies , therefore , Eq . i) becomes
` (K_("disc"))/(K_("ring")) = sqrt((1/2MR^(2))/(MR^(2))) = 1: sqrt(2)`