Question

The ratio of radii of gyration of a ring to a disc (both circular) of same radii and mass, about a tangential axis perpendicular to the plane is

Options

• `sqrt3/sqrt2`

• `2/sqrt5`

• `sqrt2/1`

• `2/sqrt3`

Answer 1

`2/sqrt3`

Explanation:

The radius of gyration is given by

K = `sqrt("l"/"M") => "K" prop sqrt"I"`

Moment of inertia of ring about tangential axis Is calculated by parallel axis theorem, l_ring = l_e + MR²

= MR² + MR² = 2MR² 

Similarly,

`"l"_"disc" = "l"_"e" + "MR"^2 = 1/2"MR"^2 + "MR"^2 = 3/2"MR"^2`

`therefore "K"_"ring"/"K"_"disc" = sqrt(("l"_"ring")/("l"_"disc")) = sqrt((2 "MR"^2)/(3/2 "MR"^2)) = 2/sqrt3`