$A$ steel wire of length $20 \text{ cm}$ and area of cross-section $1 \text{ mm}^2$ is tied rigidly at both the ends. When the temperature of the wire is changed from $40^{\circ} \text{C}$ to $20^{\circ} \text{C}$, find the change in its tension. Given, the coefficient of linear expansion for steel is $\alpha = 1.1 \times 10^{-5} {}^{\circ} \text{C}^{-1}$ and Young's modulus of steel is $Y = 2.0 \times 10^{11} \text{ N/m}^2$. (in $\text{ N}$)
- A$22$
- B$44$
- C$16$
- D$8$
Explore More
Similar Questions
At $40\,^oC$,a brass wire of radius $0.5\, mm$ (diameter $1\, mm$) is hung from the ceiling. $A$ small mass $M$ is hung from the free end of the wire. When the wire is cooled down from $40\,^oC$ to $20\,^oC$,it regains its original length of $0.2\, m$. The value of $M$ is close to ........$kg$. (Coefficient of linear expansion $\alpha = 10^{-5}/^oC$ and Young's modulus $Y = 10^{11}\, N/m^2$; $g = 10\, ms^{-2}$)
DifficultJEE MAIN 2019
View SolutionThe proportional limit of steel is $8 \times 10^8 \, N/m^2$ and its Young's modulus is $2 \times 10^{11} \, N/m^2$. The maximum elongation,a one metre long steel wire can be given without exceeding the elastic limit is ...... $mm$.
Medium
View SolutionThe elongation of a wire on the surface of the earth is $10^{-4} \; m$. The same wire of same dimensions is elongated by $6 \times 10^{-5} \; m$ on another planet. The acceleration due to gravity on the planet will be $\dots \; m/s^2$. (Take acceleration due to gravity on the surface of earth $= 10 \; m/s^2$)
One end of a metal wire is fixed to a ceiling and a load of $2 \ kg$ hangs from the other end. $A$ similar wire is attached to the bottom of the load and another load of $1 \ kg$ hangs from this lower wire. Then the ratio of longitudinal strain of the upper wire to that of the lower wire will be . . . . . . .
[Area of cross section of wire $= 0.005 \ cm^2$,$Y = 2 \times 10^{11} \ Nm^{-2}$ and $g = 10 \ ms^{-2}$]
[Area of cross section of wire $= 0.005 \ cm^2$,$Y = 2 \times 10^{11} \ Nm^{-2}$ and $g = 10 \ ms^{-2}$]
DifficultJEE MAIN 2024
View SolutionThe length of a light string is $1.4 \ m$ when the tension on it is $5 \ N$. If the tension increases to $7 \ N$,the length of the string is $1.56 \ m$. The original length of the string is . . . . . . $m$.
Vedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo