a metal ring of mass m and radius R is placed on a smooth table and is set rotating about its own axis in such a way that each part of the ring moves with speed v. find the tension in the ring

Dear student,

Let us consider a small element ‘dx’ of the ring and writing the equilibrium equations according to the figure below:


Mass per unit length of ring = M/(2**R)
Mass of the dx element = dm = dx *M/(2**R)

For equilibrium,

2T sin= dm * v²/ R

Since,= small,sin=

2T=dx *M/(2R)* v² / R
2T (dx/R) =dx *M/(2R)* v²?/ R

Tension in the ring. T= Mv²/ (4R)