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1)

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 TM. If the young's modulus of the material of the wire is Y, then   1Y is equal to (g= gravitational acceleration)


A) [(TMT)21]AMg

B) [(TMT)21]MgA

C) [1(TMT)2]AMg

D) [1(TTM)2]AMg

Answer:

Option A

Explanation:

We  know that  time period 

T=2πLg

 When additional  mass M is added to its bob

 TM=2πL+Lg

 where   L     is increase in length

 we know that

 Y=Mg/AL/L=MgLAL

        L=MgLAY

                           TM=2πL+MgLAYg

     (TMT)2=1+MgAY

 or         MgAY=(TMT)21

 or    1Y=AMg[(TMT)21]