A uniform disc of mass $M$ and radius $R$ is suspended in vertical plane from a point on its periphery. Its time period of oscillation is ........
Medium
Download our app for free and get started
(d)
It is the case of a physical pendulum.
$T=2 \pi \sqrt{\frac{I_{\text {c.o.m. }}}{m g L_{\text {com }}}}$
$I_{\text {com }}=\frac{M R^2}{2}+M R^2=\frac{3}{2} M R^2$
$L_{\text {com }}=R$
$T=2 \pi \sqrt{\frac{3 R}{2 g}}$
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.*
Kinetic energy of a particle executing simple harmonic motion in straight line is $pv^2$ and potential energy is $qx^2$, where $v$ is speed at distance $x$ from the mean position. It time period is given by the expression
A particle is vibrating in a simple harmonic motion with an amplitude of $4\, cm.$ At what displacement from the equilibrium position, is its energy half potential and half kinetic
The amplitude of a damped oscillator becomes one third in $2\, sec$. If its amplitude after $6\, sec$ is $1/n$ times the original amplitude then the value of $n$ is
A particle moves in $xy$ plane according to the law $x = a \sin \omega t$ and $y = a(1-\cos \omega t)$ where $a$ and $\omega$ are constants. The particle traces
A body is executing $S.H.M.$ When its displacement from the mean position is $4\, cm$ and $5\, cm$, the corresponding velocity of the body is $10 \,cm/sec$ and $8\, cm/sec$. Then the time period of the body is
A particle in $SHM $ is described by the displacement equation $x(t) = A\cos (\omega t + \theta ).$ If the initial $(t = 0)$ position of the particle is $1 \,cm$ and its initial velocity is $\pi $cm/s, what is its amplitude? The angular frequency of the particle is $\pi {s^{ - 1}}$
The equation of motion of a particle of mass $1\,g$ is $\frac{{{d^2}x}}{{d{t^2}}} + {\pi ^2}x = 0$ where $x$ is displacement (in $m$ ) from mean position. The frequency of oscillation is .... $s$ (in $Hz$ )