TS EAMCET · Physics · Rotational Motion
The ratio of radii of gyration of a thin circular ring and a circular disc of same radius about a tangential axis in their own planes is \(\sqrt{12}: \sqrt{\mathrm{K}}\). The value of K is
- A 10
- B 24
- C 5
- D 12
Answer & Solution
Correct Answer
(A) 10
Step-by-step Solution
Detailed explanation
\(I_{ring} = \frac{1}{2}MR^2 + MR^2 = \frac{3}{2}MR^2\) \(I_{disc} = \frac{1}{4}MR^2 + MR^2 = \frac{5}{4}MR^2\) \(\frac{k_{ring}}{k_{disc}} = \frac{\sqrt{I_{ring}/M}}{\sqrt{I_{disc}/M}} = \sqrt{\frac{3/2 \cdot R^2}{5/4 \cdot R^2}} = \sqrt{\frac{12}{10}}\)…
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