A uniform ring having mass m, radius R, cross section area of the wire A and young’s modulus Y is rotating with an angular speed `omega`(`omega` is small) on a smooth horizontal surface. Which of the following options is correct :

Options

A. Tension in the wire is `(mRomega^(2))/(2pi)`
B. Change in length of the wire is `(mR^(2) omega^(2))/(2A.Y)`
C. Change in radius of the ring is `(mR^(2)omega^(2))/(2piA.Y)`
D. elastic potential energy stored is `1/(4pi)((m^(2)omega^(4) R^(3))/(A.Y))`

Explanation

To solve the problem regarding the uniform ring rotating on a smooth horizontal surface, we need to analyze the forces acting on the ring and the effects of its rotation.

### Step-by-Step Solution:

1. **Understanding the System**:
- We have a uniform ring with mass \( m \) and radius \( R \).
- The ring has a cross-sectional area \( A \) and a Young's modulus \( Y \).
- The ring is rotating with an angular speed \( \omega \).
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