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
JEE MAIN 2020, Diffcult
Download our app for free and get started
Moment of inertia in case $(i)$ is $I _{1}$
Moment of inertia in case $(ii)$ is $I_{2}$
$I_{1}=2 M R^{2}$
$I _{2}=\frac{3}{2} MR ^{2}$
$T _{1}=2 \pi \sqrt{\frac{ I _{1}}{ Mgd }} ; T _{2}=2 \pi \sqrt{\frac{ I _{2}}{ Mgd }}$
$\frac{ T _{1}}{ T _{2}}=\sqrt{\frac{ I _{1}}{ I _{2}}}=\sqrt{\frac{2 MR ^{2}}{\frac{3}{2} MR ^{2}}}=\frac{2}{\sqrt{3}}$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1The angular amplitude of a simple pendulum is $\theta_0$. The maximum tension in its string will beView Solution
- 2The phase difference between two $SHM\,\,$ ${y_1}\, = \,10\,\sin \,\left( {10\pi t\, + \,\frac{\pi }{3}} \right)$ and ${y_2}\, = \,12\,\sin \,\left( {8\pi t\, + \,\frac{\pi }{4}} \right)$ at $t = 0.5\,s$ itView Solution
- 3A simple harmonic oscillator has a period of $0.01 \,sec$ and an amplitude of $0.2\, m$. The magnitude of the velocity in $m{\sec ^{ - 1}}$ at the centre of oscillation isView Solution
- 4The displacement of an object attached to a spring and executing simple harmonic motion is given by $ x= 2 \times 10^{-9}$ $ cos$ $\;\pi t\left( m \right)$ .The time at which the maximum speed first occurs isView Solution
- 5A simple pendulum executing $S.H.M.$ is falling freely along with the support. ThenView Solution
- 6A particle of mass $m$ performs $SHM$ along a straight line with frequency $f$ and amplitude $A.$View Solution
- 7A particle executes $S.H.M.,$ the graph of velocity as a function of displacement is :-View Solution
- 8Two simple harmonic motions are represented by the equationsView Solution
${x}_{1}=5 \sin \left(2 \pi {t}+\frac{\pi}{4}\right)$ and ${x}_{2}=5 \sqrt{2}(\sin 2 \pi {t}+\cos 2 \pi {t})$
The amplitude of second motion is ....... times the amplitude in first motion.
- 9Three masses $700g, 500g$ and $400g$ are suspended at the end of a spring a shown and are in equilibrium. When the $700g$ mass is removed, the system oscillates with a period of $3\,seconds$, when the $500g$ mass is also removed, it will oscillate with a period of .... $s$View Solution
- 10The instantaneous displacement of a simple pendulum oscillator is given by $x = A\cos \left( {\omega t + \frac{\pi }{4}} \right)$. Its speed will be maximum at timeView Solution