question_answer

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 change to \[{{T}_{M}}.\]If the Young’s modulus of the material of the wire is Y then\[\frac{1}{Y}\]is equal to: [JEE MAIN 2015] (g = gravitational acceleration)

A)  \[\left[ 1-{{\left( \frac{{{T}_{M}}}{T} \right)}^{2}} \right]\frac{A}{Mg}\]

B)  \[\left[ 1-{{\left( \frac{T}{{{T}_{M}}} \right)}^{2}} \right]\frac{A}{Mg}\]

C)  \[\left[ {{\left( \frac{{{T}_{M}}}{T} \right)}^{2}}-1 \right]\frac{A}{Mg}\]

D)       \[\left[ {{\left( \frac{{{T}_{M}}}{T} \right)}^{2}}-1 \right]\frac{Mg}{A}\]

Correct Answer: C

Solution :

[c]