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 change to $T_M$. If the young's modulus of material of the wire is Y then $\large\frac{1}{Y}$ is equal to:

Question

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