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A pendulum made of uniform wire of cross sectional area A has time period T. When an addition 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 1/Y is equal to: (g = gravitational accele

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\begin{aligned} &\text {Time period, } \mathrm{T}=2 \pi \sqrt{\frac{1}{\mathrm{g}}}\\ &\text {When additional mass } \mathrm{M} \text { is added to its bob }\\ &\mathrm{T}_{\mathrm{M}}=2 \pi \sqrt{\frac{1+\Delta 1}{\mathrm{g}}} \end{aligned}

\large \begin{array}{l} \Delta \mathrm{l}=\frac{\mathrm{Mgl}}{\mathrm{AY}} \\ \Rightarrow \mathrm{T}_{\mathrm{M}}=2 \pi \sqrt{\frac{1+\frac{\mathrm{Mg} \mathrm{l}}{\mathrm{AY}}}{\mathrm{g}}} \\ \left(\frac{\mathrm{T}_{\mathrm{M}}}{\mathrm{T}}\right)^{2}=1+\frac{\mathrm{Mg}}{\mathrm{AY}} \\ \frac{1}{\mathrm{Y}}=\frac{\mathrm{A}}{\mathrm{Mg}}\left[\left(\frac{\mathrm{T}_{\mathrm{M}}}{\mathrm{T}}\right)^{2}-1\right] \end{array}

 

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