(C) The time period of a simple pendulum is given by $T = 2\pi \sqrt{\frac{L}{g}}$.Taking the natural logarithm on both sides: $\ln T = \ln(2\pi) + \f

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(C) The time period of a simple pendulum is given by $T = 2\pi \sqrt{\frac{L}{g}}$.Taking the natural logarithm on both sides: $\ln T = \ln(2\pi) + \frac{1}{2} \ln L - \frac{1}{2} \ln g$.Differentiating with respect to temperature $\theta$: $\frac{1}{T} \frac{dT}{d\theta} = \frac{1}{2L} \frac{dL}{d\theta}$.Since $\frac{dL}{d\theta} = L\alpha$,we have $\frac{1}{T} \frac{dT}{d\theta} = \frac{1}{2L} (L\alpha) = \frac{\alpha}{2}$.Therefore,the slope $S = \frac{dT}{d\theta} = \frac{T\alpha}{2}$.Given $T = 2 \ s$,we get $S = \frac{2\alpha}{2} = \alpha$.

Class 11 Physics 1 Thermal Properties of Matter: Thermometry, Expansion and Calorimetry Thermal Expansion for Solid

Difficult

$A$ simple pendulum made of a bob of mass $m$ and a metallic wire of negligible mass has a time period $2 \ s$ at $T = 0 \ ^oC$. If the temperature of the wire is increased and the corresponding change in its time period is plotted against its temperature,the resulting graph is a line of slope $S$. If the coefficient of linear expansion of the metal is $\alpha$,then the value of $S$ is:

JEE MAIN 2016 All JEE MAIN

A
$\frac{\alpha}{2}$
B
$2\alpha$
C
$\alpha$
D
$\frac{1}{\alpha}$

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1 Thermal Properties of Matter: Thermometry, Expansion and Calorimetry

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Thermal Expansion for Solid

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Easy

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MediumMHT CET 2023

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$A$ steel tape measures the length of a copper rod as $90 \ cm$ when both are at $10 \ ^oC$. What length (in $cm$) would the tape read for the length of the rod when both are at $30 \ ^oC$? $[\alpha_{st} = 1.2 \times 10^{-5} / ^oC$ and $\alpha_{cu} = 1.7 \times 10^{-5} / ^oC]$

Difficult

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The temperature of a metal coin is increased by $100^{\circ} C$ and its diameter increases by $0.15 \%$. Its area increases by nearly (in $\%$)

MediumKVPY 2009

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$A$ bar of iron is $10 \, cm$ at $20^{\circ}C$. At $19^{\circ}C$ it will be ($\alpha$ of iron $= 11 \times 10^{-6}/^{\circ}C$)

Medium

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$A$ steel tape gives correct measurement at $20^{\circ} C$. $A$ piece of wood is being measured with the steel tape at $0^{\circ} C$. The reading is $25 \ cm$ on the tape. The real length of the given piece of wood must be:

The side of a copper cube is $1 \ m$ at $0^{\circ} C$. What will be the change in its volume,when it is heated to $100^{\circ} C$? $[\alpha_{\text{copper}} = 18 \times 10^{-6} /^{\circ} C]$

$A$ steel tape measures the length of a copper rod as $90 \ cm$ when both are at $10 \ ^oC$. What length (in $cm$) would the tape read for the length of the rod when both are at $30 \ ^oC$? $[\alpha_{st} = 1.2 \times 10^{-5} / ^oC$ and $\alpha_{cu} = 1.7 \times 10^{-5} / ^oC]$

The temperature of a metal coin is increased by $100^{\circ} C$ and its diameter increases by $0.15 \%$. Its area increases by nearly (in $\%$)

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