$A$ pendulum made of a uniform wire of cross-sectional area $A$ has a time period $T$. When an additional 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 $\frac{1}{Y}$ is equal to ($g$ = gravitational acceleration).

• A
  $\left[ {{{\left( {\frac{{{T_M}}}{T}} \right)}^2} - 1} \right]\frac{{Mg}}{A}$
• B
  $\left[ {1 - {{\left( {\frac{{{T_M}}}{T}} \right)}^2}} \right]\frac{A}{{Mg}}$
• C
  $\left[ {1 - {{\left( {\frac{T}{{{T_M}}}} \right)}^2}} \right]\frac{A}{{Mg}}$
• D
  $\left[ {{{\left( {\frac{{{T_M}}}{T}} \right)}^2} - 1} \right]\frac{A}{{Mg}}$