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 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 :

Question

$\begin{array}{1 1}(1) L \bigg( 1+ \large\frac{2}{9} \frac{Mg}{\pi YR^2} \bigg) \\ (2) L \bigg( 1+ \large\frac{1}{3} \frac{Mg}{\pi YR^2} \bigg) \\ (3) L \bigg( 1+ \large\frac{1}{9} \frac{Mg}{\pi YR^2} \bigg) \\ (4) L \bigg( 1+ \large\frac{2}{3} \frac{Mg}{\pi YR^2} \bigg) \end{array}$