The ratio of the radii of gyration of a circular disc about a tangential axis in the plane of the disc and of a circular ring of the same radius about a tangential axis in the plane of the ring is

Question

The ratio of the radii of gyration of a circular disc about a tangential axis in the plane of the disc and of a circular ring of the same radius about a tangential axis in the plane of the ring is (A)  2:3  (B)  2:1  (C)  √5:√6  (D)  1:√2

Tardigrade Admin · Accepted Answer

Radius of gyration of disc about a tangential axis in the plane of disc is

\frac{5}{2} R = K_{1}

, radius of gyration of circular ring of same radius about a tangential axis in the plane of circular ring is

K_{2} = \frac{3}{2} R

∴ \frac{K _{1}}{K _{2}} = \frac{5}{6}

Q. The ratio of the radii of gyration of a circular disc about a tangential axis in the plane of the disc and of a circular ring of the same radius about a tangential axis in the plane of the ring is

$2 : 3$

$2 : 1$

$5 : 6$

$1 : 2$

Radius of gyration of disc about a tangential axis in the plane of disc is $\frac{5}{2} R = K_{1}$ , radius of gyration of circular ring of same radius about a tangential axis in the plane of circular ring is
$K_{2} = \frac{3}{2} R$
$∴ \frac{K _{1}}{K _{2}} = \frac{5}{6}$

Q. The ratio of the radii of gyration of a circular disc about a tangential axis in the plane of the disc and of a circular ring of the same radius about a tangential axis in the plane of the ring is

2:3

2:1

5​:6​

1:2​

Radius of gyration of disc about a tangential axis in the plane of disc is 25​​R=K1​, radius of gyration of circular ring of same radius about a tangential axis in the plane of circular ring is K2​=23​​R ∴K2​K1​​=6​5​​

$2 : 3$

$2 : 1$

$5 : 6$

$1 : 2$

Radius of gyration of disc about a tangential axis in the plane of disc is $\frac{5}{2} R = K_{1}$ , radius of gyration of circular ring of same radius about a tangential axis in the plane of circular ring is
$K_{2} = \frac{3}{2} R$
$∴ \frac{K _{1}}{K _{2}} = \frac{5}{6}$