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NEET 2004
Exam
NEET
Year
2004
Subject
Physics
Chapter
Rotational Motion

NEET 2004 · Physics · Rotational Motion

The ratio of the radii of gyration of a circular disc about a...

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

  1. A2:32: 3
  2. B2:12: 1
  3. C5:6\sqrt{5}: \sqrt{6}
  4. D1:21: \sqrt{2}

Correct answer

C. 5:6\sqrt{5}: \sqrt{6}

Step-by-step solution

The radius of gyration of disc about a tangential axis in the plane of disc is k1k_1 \therefore \quad k_1=52\frac{\sqrt{5}}{2}R And radius of gyration of circular ring of same radius about tangential axis is given by: k2=32R∴k1k2=52R×23R=56\begin{aligned}k_2 & =\frac{\sqrt{3}}{2} \mathrm{R}\\ \therefore \quad \frac{k_1}{k_2}& =\frac{\sqrt{5}}{2}R \times \frac{\sqrt{2}}{\sqrt{3} R}\\ & =\frac{\sqrt{5}}{\sqrt{6}} \end{aligned}
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