A uniformly tapering conical wire is made from a material of Young's modulus Y and has a normal, unextended length L. The radii, at the upper and…

A uniformly tapering conical wire is made from a material of Young's modulus $\displaystyle Y$ and has a normal, unextended length $\displaystyle L$. The radii, at the upper and lower ends of this conical wire, have values $\displaystyle R$ and $\displaystyle 3 R$, respectively. The upper end of the wire is fixed to a rigid support and a mass $\displaystyle M$ is suspended from its lower end. The equilibrium extended length, of this wire, would equal :