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$\frac{3}{\sqrt{2}}$
JEE MAIN 2020, Diffcult
art

Download our app
and 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

  • 1
    A particle is performing $S.H.M.$ with energy of vibration $90 \,J$ and amplitude $6 \,cm$. When the particle reaches at distance $4 \,cm$ from mean position, it is stopped for a moment and then released. The new energy of vibration will be ........... $J$
    View Solution
  • 2
    A particle is subjected to two mutually perpendicular simple harmonic motions such that its $x$ and $y$ coordinates are given by ?

    $ x = 2 \sin \omega t \,;$  $ y = 2 \sin  \left( {\omega t + \frac{\pi }{4}} \right)$

    The path of the particle will be :

    View Solution
  • 3
    The particle executing simple harmonic motion has a kinetic energy $K_0cos^2 \omega t$. The maximum values of the potential energy and the total energy are respectively
    View Solution
  • 4
    Time period of a simple pendulum is $T$ inside a lift when the lift is stationary. If the lift moves upwards with an acceleration $g / 2,$ the time period of pendulum will be
    View Solution
  • 5
    Two simple pendulums of length $0.5\, m$ and $2.0\, m$ respectively are given small linear displacement in one direction at the same time. They will again be in the phase when the pendulum of shorter length has completed .... oscillations.
    View Solution
  • 6
    A pendulum bob is swinging in a vertical plane such that its angular amplitude is less than $90^o$. At its highest point, the string is cut. Which trajectory is possible for the bob afterwards.
    View Solution
  • 7
    In forced oscillations, a particle oscillates simple harmonically with a frequency equal to
    View Solution
  • 8
    The composition of two simple harmonic motions of equal periods at right angle to each other and with a phase difference of $\pi $ results in the displacement of the particle along
    View Solution
  • 9
    The length of a simple pendulum is increased by $2\%$. Its time period will
    View Solution
  • 10
    A particle is executing $S.H.M.$ and its velocity $v$ is related to its position $(x)$ as $v^2+a x^2=b$, where $a$ and $b$ are positive constants. The frequency of oscillation of particle is ..........
    View Solution