A ring of diameter $2m$ oscillates as a compound pendulum about a horizontal axis passing through a point at its rim. It oscillates such that its centre move in a plane which is perpendicular to the plane of the ring. The equivalent length of the simple pendulum is .... $m$
Diffcult
Download our app for free and get started
$\mathrm{T}=2 \pi \sqrt{\frac{\mathrm{I}}{\mathrm{mgl}}}=\sqrt{\frac{3 \mathrm{mr}^{2}}{2 \mathrm{mgr}}}$
or $T=2 \pi \sqrt{\frac{3 r}{2 m}}$
or $2 \pi \sqrt{\frac{l}{\mathrm{g}}}=2 \pi \sqrt{\frac{3 \mathrm{r}}{2 \mathrm{g}}}$
$\therefore \quad l=\frac{3}{2} \mathrm{r}=\frac{3}{2} \times 1=1.5 \mathrm{m}$
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
- 1A particle performs $SHM$ about $x = 0$ such that at $t = 0$ it is at $x = 0$ and moving towards positive extreme. The time taken by it to go from $x = 0$ to $x = \frac{A}{2}$ is ..... times the time taken to go from $x = \frac{A}{2}$ to $A$. The most suitable option for the blank space isView Solution
- 2A uniform thin ring of radius $R$ and mass $m$ suspended in a vertical plane from a point in its circumference. Its time period of oscillation is ........View Solution
- 3Assuming all pulleys, springs and string massless. Consider all surface smooth. Choose the correct statement $(s)$View Solution
- 4A simple pendulum of length $l$ and mass $m$ of the bob is suspended in a car that is travelling with a constant speed $v$ around a circular path of radius $R$. If the pendulum undergoes oscillations with small amplitude about its equilibrium position, the frequency of its oscillations will beView Solution
- 5A pendulum has time period $T$ in air. When it is made to oscillate in water, it acquired a time period $T' = \sqrt 2 T$. The density of the pendulum bob is equal to (density of water $= 1$)View Solution
- 6The average speed of the bob of a simple pendulum oscillating with a small amplitude $A$ and time period $T$ isView Solution
- 7A mass of $0.2\,kg$ is attached to the lower end of a massless spring of force-constant $200\, N/m,$ the upper end of which is fixed to a rigid support. Which of the following statements is/are true ?View Solution
- 8The kinetic energy of a particle executing $S.H.M.$ is $16\, J$ when it is at its mean position. If the mass of the particle is $0.32 \,kg$, then what is the maximum velocity of the particle ..... $m/s$View Solution
- 9A simple pendulum is suspended in a car. The car starts moving on a horizontal road according to equation $x\, = \,\frac{g}{2}\,\sqrt 3 {t^2}$. Find the time period of oscillation of the pendulum.View Solution
- 10A particle is performing $SHM$ according to the equation $x = (3\, cm)$ $\sin \,\left( {\frac{{2\pi t}}{{18}} + \frac{\pi }{6}} \right)$ where $t$ is in seconds. The distance travelled by the particle in $36\, s$ is ..... $cm$View Solution