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

$A$ steel rod of length $1\,m$ and area of cross-section $1\,cm^2$ is heated from $0\,^{\circ}C$ to $200\,^{\circ}C$ without being allowed to extend or bend. Find the tension produced in the rod $(Y = 2.0 \times 10^{11}\,N/m^2, \alpha = 10^{-5} \,^{\circ}C^{-1})$.

The following four wires of length $L$ and radius $r$ are made of the same material. Which of these will have the largest extension,when the same tension is applied?

What is the effect of change in temperature on the Young's modulus?

Write the equation of bending in a rod. Write the unit of bending and its dimensional formula.

When a wire of length $L$ clamped at one end is pulled by a force $F$ from the other end,its length increases by $l$. If the radius of the wire and the applied force were halved,then the increase in its length is

Vedclass Test Series

Exam Paper Generator

Online Exam Module