Rotational Motion Question 194
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
Options:
A) $1:\sqrt{2}$
B) l : 3
C) 2: l
D) $\sqrt{5}:\sqrt{6}$
Show Answer
Answer:
Correct Answer: D
Solution:
[d]
$ I _{y_1}=\frac{M R^2}{4} $
$ \therefore I^{\prime} y_1=\frac{M R^2}{4}+M R^2=\frac{5}{4} M R^2 .$
$ I _{y_2}=\frac{M R^2}{2} $
$ \therefore I _{y_2}^{\prime}=\frac{M R^2}{2}+M R^2=\frac{3}{2} M R^2 $
$ I^{\prime} y_1=M K_1^2, I^{\prime} y_2=M K_2^2 $
$ \therefore \quad \frac{K_1^2}{K_2^2}=\frac{I _{y_1}^{\prime}}{I^{\prime} y_2} \Rightarrow K_1: K_2=\sqrt{5}: \sqrt{6} $
