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A uniformly tapering conical wire is made from a material of Youngs’s and has a normal, unextended length L. The radii, at the upper and lower ends of this conical wire, have values R and 3R, respectively. The upper end of the wire is fixed to a rigid support and a mass M is suspended from its lower end. The equilibrium extended length, of this wire, would equal :
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Correct option is A
Take a cross-section taken at a point x from the bottom; hence, at this point,
where dy is the elongation of the portion dx.
As we solve for x in the range of 0 to L, we obtain,
Hence the correct answer is
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