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  • 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 TM. If  the Young&

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 TM. If  the Young’s modulus of the material of the

 wire is Y then \frac{1}{Y} is equal to :

(g=gravitational acceleration)

Option: 1

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


Option: 2

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


Option: 3

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


Option: 4

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


Answers (1)

best_answer

\text {Time period} ,\\\mathrm{T}=2 \pi \sqrt{\frac{l}{g}}$\\ When additional mass $M$ is added to its bob\\ $T_{M}=2 \pi \sqrt{\frac{l+\Delta l}{g}}$

\begin{aligned} &\Delta l=\frac{M g l}{A Y}\\ &\Rightarrow T_{M}=2 \pi \sqrt{\frac{l+\frac{M g l}{A Y}}{g}} \end{aligned}

\begin{aligned} &\left(\frac{T_{M}}{T}\right)^{2}=1+\frac{M g}{A Y}\\ &\frac{1}{Y}=\frac{A}{M g}\left[\left(\frac{T_{M}}{T}\right)^{2}-1\right] \end{aligned}

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Riya

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