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Heat and Temperature — Physics STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 SciencePhysicsHeat and Temperature5 Marks
Question
A torsional pendulum consists of a solid disc connected to a thin wire$\Big(\alpha=2.4\times10^{-5}\ ^\circ\text{C}^{-1}\Big)$at its centre. Find the percentage change in the time period between peak winter (5°C) and peak summer (45°C).
✓

Answer

Let the initial m.I. at 0°C be $\text{I}_0$

$\text{T}=2\pi\sqrt\frac{\text{I}}{\text{K}}$

$\text{I}=\text{I}_0(1+2\alpha\Delta\theta)$ (from above question)

At 5°C, $\text{T}_1=2\pi\sqrt\frac{\text{I}_0(1+2\alpha\Delta\theta)}{\text{K}}$

$=2\pi\sqrt\frac{\text{I}_0(1+2\alpha\Delta5)}{\text{k}}$

$=2\pi\sqrt\frac{\text{I}_0(1+10\alpha)}{\text{K}}$

At 45°C, $\text{T}_2=2\pi\sqrt\frac{\text{I}_0(1+2\alpha45)}{\text{K}}$

$2\pi\sqrt\frac{\text{I}_0(1+90\alpha)}{\text{K}}$

$\frac{\text{T}_2}{\text{T}_1}=\sqrt\frac{1+90\alpha}{1+10\alpha}$

$=\sqrt\frac{1+90\times2.4\times10^{-5}}{1+10\times2.4\times10^{-5}}\sqrt\frac{1.00216}{1.00024}$

% change $=\Big(\frac{\text{T}_2}{\text{T}_1}-1\Big)\times100$

$=0.0959\%=9.6\times10^{-2}\%$

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