Rotational Motion Question 65
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
[AIPMPT (S) 2008]
Options:
A) $ \sqrt{3}:\sqrt{2} $
B) $ 1:\sqrt{2} $
C) $ \sqrt{2}:1 $
D) $ \sqrt{2}:\sqrt{3} $
Show Answer
Answer:
Correct Answer: B
Solution:
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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}MR^{2} $
and $ I _{ring} $ (about its axis) $ =MR^{2} $ where R is the radius of both bodies.
Therefore, Eq.
(i) becomes
$ \frac{K _{disc}}{K _{ring}}=\sqrt{\frac{\frac{1}{2}MR^{2}}{MR^{2}}}=1:\sqrt{2} $
