Question

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

• A. 2 : 3
• B. 2 : 1
• C. $\sqrt { 5 } : \sqrt { 6 }$
• D. $1 : \sqrt { 2 }$

Answer 1

Answer: (C)

$\sqrt { 5 } : \sqrt { 6 }$

Answer 2

M.I. of disc about a tangent in a plane

= $\frac { 5 } { 4 } m r ^ { 2 }$

$m K _ { d } ^ { 2 } = \frac { 5 } { 4 } m r ^ { 2 }$ ⇒ $K _ { d } \sqrt { \frac { 5 } { 4 } } r$

M.I. of ring about a tangent in a plane =$\frac { 3 } { 2 } m r ^ { 2 }$

$m K _ { r } ^ { 2 } = \frac { 3 } { 2 } m r ^ { 2 }$ ⇒ $K _ { r } = \sqrt { \frac { 3 } { 2 } } r$

∴ Ratio of radius of gyration $\frac { K _ { d } } { K _ { r } } = \frac { \sqrt { 5 / 4 } r } { \sqrt { 3 / 2 } r } = \sqrt { \frac { 5 } { 6 } }$