Question

The ratio of radius of gyration of a ring to circular disc of same radii and mass about a tangential axis perpendicular to the plane is ______.

Options

• `3/2`

• `2/3`

• `1/sqrt 3`

• `2/sqrt 3`

Answer 1

The ratio of radius of gyration of a ring to circular disc of same radii and mass about a tangential axis perpendicular to the plane is `bbunderline(2/sqrt 3)`.

Explanation:

For a tangential axis perpendicular to the plane, use the parallel axis theorem:

For ring:

I = `I_"center" + MR^2`

= MR² + MR²

= 2MR²

k_ring = `sqrt (I/M)`

= `sqrt 2 R`

For disc:

I = `1/2 MR^2 + MR^2`

= `3/2 MR^2`

k_disc = `sqrt 3/2 R`

`k_"ring"/k_"disc" = (sqrt 2 R)/(sqrt (3/2) R)`

= `2/sqrt 3`