Answer
Verified
377.1k+ views
Hint: Young’s modulus describes the relationship between stress (force per unit area) and strain (proportional deformation in an object. The Young’s modulus is named after the British scientist Thomas Young. A solid object deforms when a particular load is applied to it.
Complete step by step answer:
Given, Original length of telephone wire, $l = 125\,m$
Length after stretched, ${l_f} = 125.25\,m$
Radius of telephone wire, $r = 1\,mm$
Radius of telephone wire, $r = 0.001\,m$
Cross section area of telephone wire,
$\therefore A = \pi {r^2}$
Put the value
\[ A = \dfrac{{22}}{7} \times {(0.001)^2}\]
$ \Rightarrow 3.14 \times {10^{ - 6}}$
Change in length, $\Delta l = ?$
$\therefore \Delta l = {l_f} - l$
Put the value
$ \Delta l = 125.25 - 125$
$ \Rightarrow \Delta l = 0.25\,m$
Strain in telephone wire, $\varepsilon = ?$
As we know that
$\varepsilon = \dfrac{{\Delta l}}{l}$
Put the value
$ \varepsilon = \dfrac{{0.25}}{{125}} \\$
$ \Rightarrow \varepsilon = 0.002$
Now
Young’s modulus,
$Y = \dfrac{{\dfrac{F}{A}}}{{\dfrac{{\Delta l}}{l}}}$
Put the value
$Y = \dfrac{{\dfrac{{800}}{{3.14 \times {{10}^6}}}}}{{\dfrac{{0.25}}{{125}}}} \\$
Simplify
$\Rightarrow Y = \dfrac{{800 \times 125}}{{3.14 \times {{10}^{ - 6}} \times 0.25}} \\$
$\therefore Y = 1.27 \times {10^{11}}Pa$
Hence, the value of Young’s modulus for material wire is $1.27 \times {10^{11}}\,Pa$.
Note: The young’s modulus of a material is a fundamental property of every material that cannot be changed. It is dependent upon temperature and pressure however. The young’s modulus is the essence, the stiffness of a material. In other words, it is how easily it is bended or stretched.
Complete step by step answer:
Given, Original length of telephone wire, $l = 125\,m$
Length after stretched, ${l_f} = 125.25\,m$
Radius of telephone wire, $r = 1\,mm$
Radius of telephone wire, $r = 0.001\,m$
Cross section area of telephone wire,
$\therefore A = \pi {r^2}$
Put the value
\[ A = \dfrac{{22}}{7} \times {(0.001)^2}\]
$ \Rightarrow 3.14 \times {10^{ - 6}}$
Change in length, $\Delta l = ?$
$\therefore \Delta l = {l_f} - l$
Put the value
$ \Delta l = 125.25 - 125$
$ \Rightarrow \Delta l = 0.25\,m$
Strain in telephone wire, $\varepsilon = ?$
As we know that
$\varepsilon = \dfrac{{\Delta l}}{l}$
Put the value
$ \varepsilon = \dfrac{{0.25}}{{125}} \\$
$ \Rightarrow \varepsilon = 0.002$
Now
Young’s modulus,
$Y = \dfrac{{\dfrac{F}{A}}}{{\dfrac{{\Delta l}}{l}}}$
Put the value
$Y = \dfrac{{\dfrac{{800}}{{3.14 \times {{10}^6}}}}}{{\dfrac{{0.25}}{{125}}}} \\$
Simplify
$\Rightarrow Y = \dfrac{{800 \times 125}}{{3.14 \times {{10}^{ - 6}} \times 0.25}} \\$
$\therefore Y = 1.27 \times {10^{11}}Pa$
Hence, the value of Young’s modulus for material wire is $1.27 \times {10^{11}}\,Pa$.
Note: The young’s modulus of a material is a fundamental property of every material that cannot be changed. It is dependent upon temperature and pressure however. The young’s modulus is the essence, the stiffness of a material. In other words, it is how easily it is bended or stretched.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Which are the Top 10 Largest Countries of the World?
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Change the following sentences into negative and interrogative class 10 english CBSE
How do you graph the function fx 4x class 9 maths CBSE
Write a letter to the principal requesting him to grant class 10 english CBSE