A) \[\sqrt{3}:\sqrt{2}\]
B) \[1:\sqrt{2}\]
C) \[\sqrt{2}:1\]
D) \[\sqrt{2}:\sqrt{3}\]
Correct Answer: B
Solution :
Key Idea: The square root of the ratio of the moment of inertia of a rigid body and its mass is called radius of gyration. As in key idea, radius of gyration is given by \[K=\sqrt{\frac{I}{M}}\]For given problem \[\frac{{{K}_{disc}}}{{{K}_{ring}}}=\sqrt{\frac{{{I}_{disc}}}{{{I}_{ring}}}}\] But \[{{I}_{disc}}\](about its axis) \[=\frac{1}{2}M{{R}^{2}}\] and \[{{I}_{ring}}\] (about its axis) \[=M{{R}^{2}}\]where R is the radius of both bodies. Therefore, Eq. (i) becomes \[\frac{{{K}_{disc}}}{{{K}_{ring}}}=\sqrt{\frac{\frac{1}{2}M{{R}^{2}}}{M{{R}^{2}}}}=1:\sqrt{2}\]
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