(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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(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 10-1.Thermometry, Thermal 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
$\frac{1}{\alpha}$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Physics Questions

Chapter

10-1.Thermometry, Thermal Expansion and Calorimetry

Subtopic

Thermal Expansion for Solid

Previous Year

JEE MAIN 2016 Paper All JEE MAIN years →

$A$ steel scale measures the length of a copper wire as $80.0\,cm$ when both are at $20^\circ C$ (the calibration temperature for the scale). What would be the scale reading for the length of the wire when both are at $40^\circ C$ (in $,cm$)?

Medium

View Solution

An aluminium and steel rod having same lengths and cross-sections are joined to make a total length of $120 \ cm$ at $30^{\circ} C$. The coefficients of linear expansion of aluminium and steel are $24 \times 10^{-6} /{ }^{\circ} C$ and $1.2 \times 10^{-5} /{ }^{\circ} C$,respectively. The length of this composite rod when its temperature is raised to $100^{\circ} C$,is . . . . . . $cm$. (in $cm$)

DifficultJEE MAIN 2026

View Solution

The coefficient of volume expansion of a material is $5 \times 10^{-4} {^{\circ}C}^{-1}$. The fractional change in its density for a $40^{\circ}C$ rise in temperature is nearly.

EasyAP EAMCET 2022

View Solution

The ratio of linear expansion coefficient,area expansion coefficient,and volume expansion coefficient is ...............

Medium

View Solution

Two rods,one of copper $(Cu)$ and the other of iron $(Fe)$,having initial lengths $L_1$ and $L_2$ respectively,are connected together to form a single rod of length $L_1+L_2$. The coefficients of linear expansion of $Cu$ and $Fe$ are $\alpha_c$ and $\alpha_i$ respectively. If the length of each rod increases by the same amount when their temperatures are raised by $t^{\circ}C$,then the ratio $\frac{L_1-L_2}{L_1+L_2}$ will be:

DifficultMHT CET 2024

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

Similar Questions

$A$ steel scale measures the length of a copper wire as $80.0\,cm$ when both are at $20^\circ C$ (the calibration temperature for the scale). What would be the scale reading for the length of the wire when both are at $40^\circ C$ (in $,cm$)?

The coefficient of volume expansion of a material is $5 \times 10^{-4} {^{\circ}C}^{-1}$. The fractional change in its density for a $40^{\circ}C$ rise in temperature is nearly.

The ratio of linear expansion coefficient,area expansion coefficient,and volume expansion coefficient is ...............

Vedclass Test Series

Exam Paper Generator

Online Exam Module