Change in the time period of a pendulum

[Prabs3257]

Homework Statement

3.A pendulum made of a uniform wire of cross ` sectional area `A` has 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 `(1)/Y` is equal to ` `

Relevant Equations

T=2π√l/g

I tried taking log and then diffrentiate the standard equation for time period of a pendulum but i am not getting the correct answer

 

[PeroK]

The period of a pendulum depends on its length. I don't understand your method at all.

Can you relate the new length of the pendulum (with mass $M$) to the old length (without mass $M$)?