A thin uniform metallic rod of length 0.5 m and radius 0.1 m rotates with an angular velocity 400rad/s is a horizontal plane about a vertical axis passing through one of its ends. Calculate (a) tenstion in the rod and (b) the elogation of te rod. The density of material of the rod is `10^(4)kg//m^(3)` and the young's modulus is `2xx10^(11)N//m^(2)`

Explanation

To solve the problem step by step, we will first calculate the tension in the rod and then the elongation of the rod.

### Given Data:
- Length of the rod, \( L = 0.5 \, \text{m} \)
- Radius of the rod, \( r = 0.1 \, \text{m} \)
- Angular velocity, \( \omega = 400 \, \text{rad/s} \)
- Density of the material, \( \rho = 10^4 \, \text{kg/m}^3 \)
- Young's modulus, \( Y = 2 \times 10^{11} \, \text{N/m}^2 \)
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