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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

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

Grade:12th pass

1 Answers

Shobhit Varshney IIT Roorkee
askIITians Faculty 33 Points
7 years ago
Dear student,

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

256-763_shear modulus.jpg
Mass per unit length of ring = M/(2*\Pi*R)
\RightarrowMass of the dx element = dm = dx *M/(2*\Pi*R)

For equilibrium,

2T sin\Theta= dm * v2/ R

Since,\Theta= small,sin\Theta=\Theta

\Rightarrow2T\Theta=dx *M/(2\PiR)* v2 / R
2T (dx/R) =dx *M/(2\PiR)* v2?/ R

\RightarrowTension in the ring. T= Mv2/ (4\PiR)

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