There is some change $W$ length when a $ 33000 \, N$ tensile force is applied on a steel rod of area of cross-section $10^{-3} \, m^2$. The change of temperature required to produce the same elongation, if the steel rod is heated, is (The modulus of elasticity is $3 \times 10^{11} N/m^2$ and the coefficient of linear expansion of steel is $ 1.1 \times 10^{-5} /^{\circ} C)$.
- $20^{\circ} C $
- $15^{\circ} C $
- $10^{\circ} C $
- $0^{\circ} C $
The Correct Option is C
Solution and Explanation
$=\frac{\text { Force }}{\text { Area }} \times \frac{l}{\Delta l}$
$3 \times 10^{11}=\frac{33000}{10^{-3}} \times \frac{l}{\Delta l}$
$\frac{\Delta l}{l}=\frac{33000}{10^{-3}} \times \frac{1}{3 \times 10^{11}}$
$=11 \times 10^{-5}$
Change in length, $\frac{\Delta l}{l}=\alpha \Delta T$
$11 \times 10^{-5}=1.1 \times 10^{-5} \times \Delta T$
$\Rightarrow \Delta T=10\, K$ or $10^{\circ} C$
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Concepts Used:
Stress and Strain
Stress and Strain are the terms in physics, which are used to explain deformation of solids.
What is Stress?
Force applied per unit area is known as stress.
- σ=F/A
- σ is stress applied
- F is force applied
- A is that the area of force applied
- Stress is measured by unit N/m2
What is Strain?
As a result of stress, change of shape is observed in the body. The change or deformity consequential to the stress acting on the body is called strain. Strain can be defined as the amount or measure of deformity that takes place due to the force applied on the object.
Strain is denoted with (ε). It has no units.
Longitudinal Strain = Δ L/L
Relation Between Stress and Strain
The English scientist Robert Hooke, while studying spring and elasticity, noticed that many materials displayed an identical property when the stress-strain relationship was studied. There exists a linear region where the force required to stretch the material was proportional to the extension of the material; this is called Hooke’s law. Mathematically, the law is presented as:
F = -k.x
Where, F = the force
x = the extension length
k = spring constant in N/m
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