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A thin uniform metallic rod of length 0.5 m and radius 0.1 m rotates with angular velocity 400 rad/s in a horizontal plane about a vertical axis through one of its ends. The density of the rod material is 10⁴ kg/m³ and Young's modulus is 2 * 10¹¹ N/m². Which of the following statement(s) is/are correct?
- The elongation of the rod is (1/3) * 10⁻³ m.
- The elongation of the rod is non-uniform along its length.
- Tension at the centre of the rod is (3*pi/2) * 10⁶ N.
- Tension at the centre of the rod is (2*pi/2) * 10⁶ N.
Correct answer: The elongation of the rod is (1/3) * 10⁻³ m.
Solution
The elongation of a rotating rod about one end is rho*omega²*L³/(3Y). Substituting values gives (1/3)*10⁻³ m. The elongation per unit length varies (non-uniform), but the total elongation matches option A.
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