Question

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:

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

Answer 1

Answer: (D)

1 : $\sqrt { 2 }$

Answer 2

For disc, K₁ = $\sqrt { \frac { \mathrm { I } } { \mathrm { M } } }$ = = $\frac { \mathrm { R } } { \sqrt { 2 } }$

For Ring, K₂ = $\sqrt { \frac { \mathrm { I } } { \mathrm { M } } }$ = $\sqrt { \frac { \mathrm { MR } ^ { 2 } } { \mathrm { M } } }$ = R

Þ = $\frac { 1 } { \sqrt { 2 } }$