A pendulum made of a uniform wire of cross sectional area A has time period T. When an addition mass M is added to its bob, the time period changes to $T_M$. If the young's modulus of the material of the wire is Y then $\large\frac{1}{Y}$ is equal to : (g = gravitational acceleration)

Question

$\begin{array}{1 1} \bigg[\bigg(\frac{T_M}{T}\bigg)-1 \bigg]\frac{Mg}{A} \\ \bigg[1-\bigg(\frac{T_M}{T}\bigg)^2\bigg] \frac{A}{Mg} \\ \bigg[1- \bigg(\frac{T}{T_M}\bigg)^2\bigg]\frac{A}{Mg} \\ \bigg[\bigg(\frac{T_M}{T} \bigg)^2 - 1 \bigg]\frac{A}{M_g} \end{array}$