(D) When a rod is fixed at both ends,its thermal expansion is prevented,resulting in thermal stress.Thermal strain is given by $\epsilon = \frac{\Delt

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

(D) When a rod is fixed at both ends,its thermal expansion is prevented,resulting in thermal stress.Thermal strain is given by $\epsilon = \frac{\Delta L}{L} = \alpha \cdot \Delta T$.According to Hooke's Law,Stress $\sigma = Y \cdot \text{Strain}$.Substituting the strain value,we get $\sigma = Y \cdot \alpha \cdot \Delta T$.Since $Y$,$\alpha$,and $\Delta T$ are the factors determining the stress,the stress is independent of the length $L$ of the rod.Therefore,the correct statement is that the stress is independent of $L$.

Class 11 Physics Mechanical Properties of Solids Young’s Modulus

Easy

$A$ metal rod is fixed rigidly at two ends so as to prevent its thermal expansion. If $L$,$\alpha$,and $Y$ denote the length of the rod,the coefficient of linear thermal expansion,and the Young's modulus of its material respectively,then for an increase in temperature of the rod by $\Delta T$,the longitudinal stress developed in the rod is

WBJEE 2014 All WBJEE

A
inversely proportional to $\alpha$
B
inversely proportional to $Y$
C
directly proportional to $\Delta T$
D
independent of $L$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Physics Questions

Chapter

Mechanical Properties of Solids

Subtopic

Young’s Modulus

Previous Year

WBJEE 2014 Paper All WBJEE years →

In which case is there maximum extension in the wire,if the same force is applied to each wire?

Medium

View Solution

The density of a rubber cord is $d$. $A$ thick rubber cord of length $L$ and cross-sectional area $A$ undergoes elongation under its own weight when suspended vertically. This elongation is proportional to:

Medium

View Solution

$A$ metallic rod having area of cross-section $A$,Young's modulus $Y$,coefficient of linear expansion $\alpha$,and length $L$ is tied between two strong pillars. If the rod is heated through a temperature $t \, ^\circ C$,then how much force is produced in the rod?

Easy

View Solution

In Young's experiment,if the length of the wire and the radius are both doubled,then the value of $Y$ will become:

Easy

View Solution

$A$ uniform plank of Young's modulus $Y$ is moved over a smooth horizontal surface by a constant horizontal force $F$. The area of cross-section of the plank is $A$. The compressive strain on the plank in the direction of the force is

Easy

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

In which case is there maximum extension in the wire,if the same force is applied to each wire?

The density of a rubber cord is $d$. $A$ thick rubber cord of length $L$ and cross-sectional area $A$ undergoes elongation under its own weight when suspended vertically. This elongation is proportional to:

$A$ metallic rod having area of cross-section $A$,Young's modulus $Y$,coefficient of linear expansion $\alpha$,and length $L$ is tied between two strong pillars. If the rod is heated through a temperature $t \, ^\circ C$,then how much force is produced in the rod?

In Young's experiment,if the length of the wire and the radius are both doubled,then the value of $Y$ will become:

$A$ uniform plank of Young's modulus $Y$ is moved over a smooth horizontal surface by a constant horizontal force $F$. The area of cross-section of the plank is $A$. The compressive strain on the plank in the direction of the force is

Vedclass Test Series

Exam Paper Generator

Online Exam Module