JEE Mains · Physics · STD 11 - 13. oscillations
A ring is hung on a nail. It can oscillate, without slipping or sliding \((i)\) in its plane with a time period \(T_{1}\) and, \((ii)\) back and forth in a direction perpendicular to its plane, with a period \(T _{2}\). the ratio \(\frac{ T _{1}}{ T _{2}}\) will be
- A \(\frac{2}{\sqrt{3}}\)
- B \(\frac{\sqrt{2}}{3}\)
- C \(\frac{2}{3}\)
- D \(\frac{3}{\sqrt{2}}\)
Answer & Solution
Correct Answer
(A) \(\frac{2}{\sqrt{3}}\)
Step-by-step Solution
Detailed explanation
Moment of inertia in case \((i)\) is \(I _{1}\) Moment of inertia in case \((ii)\) is \(I_{2}\) \(I_{1}=2 M R^{2}\) \(I _{2}=\frac{3}{2} MR ^{2}\) \(T _{1}=2 \pi \sqrt{\frac{ I _{1}}{ Mgd }} ; T _{2}=2 \pi \sqrt{\frac{ I _{2}}{ Mgd }}\)…
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