Is it Waves?

Tension comes out to be $T =$ $\mu gr$ . .... $\mu$ is mass per unit length...

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Finding tension ------ consider an element $ds =$ $r2d$ $\theta$ on the ring

For it $2Tsind$ $\theta$ = $\frac{N}{\sqrt {2}}$

And $\frac{N}{\sqrt {2}}$ = $dmg$ = $\mu ds$ = $\mu$ $r2d$ $\theta$

$d \theta$ is very small therefore $sind \theta$ = $d \theta$

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...speed of transverse waves is $v =$ $\sqrt {T / \mu }$ ....putting values we get $\boxed{v = \sqrt{2.5 \times 10} = 5.0}$

If the cone were to be to rotated by an angular speed $\omega$ by analysis of forces we show that $T$ = $M(gcot\theta + \omega^{2}r)/2\pi$ . Here put $\omega$ equal to zero , since ring is in equilibrium. Now speed of transverse wave speed is given by $\zeta$ = $\sqrt{T/\mu}$ . Where $\mu$ is linear mass density of ring = $M/2\pi r$ . Plugging in the values we get $\zeta$ = $\boxed{5}$ .