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
Option: 1 \frac{\sqrt{2}}{3}
Option: 2 \frac{2}{3}
Option: 3 \frac{2}{\sqrt{3}}
Option: 4 \frac{3}{\sqrt{2}}

Answers (1)

Correct Answer: c) \frac{2}{\sqrt{3}}

\frac{T_1}{T_2}=\sqrt{\frac{I_1}{I_2}}

I_1=MR^2+MR^2=2MR^2

I_2=\frac{MR^2}{2}+MR^2=\frac{3}{2}MR^2

\frac{T_1}{T_2}=\sqrt{\frac{I_1}{I_2}}=\sqrt{\frac{2*2}{3}}=\frac{2}{\sqrt{3}}

 

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