A metallic rod 1 , cm long with a square cros | vedclass

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

Question

(A) The thermal expansion of the rod is given by $\Delta l = l \alpha \Delta t$,where $\Delta t$ is the change in temperature.Given $\Delta t = 1^{\ci

Vedclass · Accepted Answer

$EA\alpha t$

Vedclass · Answer

(A) The thermal expansion of the rod is given by $\Delta l = l \alpha \Delta t$,where $\Delta t$ is the change in temperature.Given $\Delta t = 1^{\circ} C$,so $\Delta l = l \alpha$.Young's modulus $E$ is defined as $E = \frac{	ext{Stress}}{	ext{Strain}} = \frac{F/A}{\Delta l / l}$.To prevent expansion,the compressional force $F$ must produce a strain equal to the thermal strain.Thus,$\frac{F}{A} = E 	imes \frac{\Delta l}{l}$.Substituting $\Delta l = l \alpha \Delta t$,we get $\frac{F}{A} = E 	imes \frac{l \alpha \Delta t}{l} = E \alpha \Delta t$.Since $\Delta t = 1$,the force is $F = EA\alpha$.

Similar Questions

$A$ $5\, m$ long aluminium wire $(Y = 7 \times 10^{10}\, N/m^2)$ of diameter $3\, mm$ supports a $40\, kg$ mass. In order to have the same elongation in a copper wire $(Y = 12 \times 10^{10}\, N/m^2)$ of the same length under the same weight,the diameter should now be,in $mm$.

$A$ steel wire of length $L$ and area of cross-section $A$ is suspended from a rigid support. If $Y$ is the Young's modulus of the material of the wire and $\alpha$ is the coefficient of linear expansion,then the increase in tension when the temperature falls by $t^{\circ} C$ is:

On applying a stress of $20 \times 10^8 \ N/m^2$,the length of a perfectly elastic wire is doubled. Its Young's modulus will be:

$A$ force $F$ is applied on a wire of radius $r$ and length $L$,and the change in the length of the wire is $l$. If the same force $F$ is applied on a wire of the same material with radius $2r$ and length $2L$,then what is the change in the length of the second wire?

The force constant of a wire does not depend on

Vedclass Test Series

Exam Paper Generator

Online Exam Module