System of Particles and Rotational Motion - Result Question 59
66. 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 [2004]
(a) $1: \sqrt{2}$
(b) $1: 3$
(c) $2: 1$
(d) $\sqrt{ } 5: \sqrt{ } 6$
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Answer:
Correct Answer: 66. (d)
Solution:
(d)
$I _{y_1}=\frac{M R^{2}}{4} \quad \therefore I_y_1^{\prime}=\frac{M R^{2}}{4}+M R^{2}=\frac{5}{4} M R^{2}$
So, if moment of inertia $(mr^{2})$ decreases K.E. of rotation increases and vice versa.
