JEE PYQ: Oscillations Question 24
Question 24 - 2020 (05 Sep 2020 Shift 2)
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:
(1) $\frac{2}{\sqrt{3}}$
(2) $\frac{2}{3}$
(3) $\frac{3}{\sqrt{2}}$
(4) $\frac{\sqrt{2}}{3}$
Show Answer
Answer: (1)
Solution
$I_1 = 2MR^2$, $I_2 = \frac{3}{2}MR^2$. $\frac{T_1}{T_2} = \sqrt{\frac{I_1}{I_2}} = \frac{2}{\sqrt{3}}$.
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