AP EAMCET · PHYSICS · Rotational Motion
If the radius of gyration of a thin circular ring about an axis passing through its centre and perpendicular to its plane is \(10 \sqrt{2} \mathrm{~cm}\), then its radius of gyration about its diameter is
- A 10 cm
- B 20 cm
- C \(10 \sqrt{2} \mathrm{~cm}\)
- D \(20 \sqrt{2} \mathrm{~cm}\)
Answer & Solution
Correct Answer
(A) 10 cm
Step-by-step Solution
Detailed explanation
\(k_z = R \Rightarrow R = 10 \sqrt{2} \mathrm{~cm}\) \(I_d = \frac{1}{2} I_z = \frac{1}{2} MR^2 \Rightarrow Mk_d^2 = \frac{1}{2} MR^2 \Rightarrow k_d = \frac{R}{\sqrt{2}}\) \(k_d = \frac{10 \sqrt{2}}{\sqrt{2}} = 10 \mathrm{~cm}\)
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