System of Particles and Rotational Motion - Result Question 59

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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]

======= ####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]

3e0f7ab6f6a50373c3f2dbda6ca2533482a77bed:content/english/neet-pyq-chapterwise/physics/system-of-particles-and-rotational-motion/system-of-particles-and-rotational-motion—result-question-59.md (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.