JEE Main 2016 Physics question
A uniformly tapering conical wire is made from a material of Young's modulus and has a normal, unextended length . The radii, at the upper and lower ends of this conical wire, have values and , respectively. The upper end of the wire is fixed to a rigid support and a mass is suspended from its lower end. The equilibrium extended length, of this wire, would equal:
Answer: (3)
Solution
The tension is the same everywhere, , but the cross-section changes along the wire, so the extension must be integrated. At a distance from the upper end the radius is , and the extension of the element is .
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