Answer :
Answer:
Cable B will more stretch the most.
Explanation:
Given that,
Length of material A =[tex]l_{A}[/tex]
Length of material B =[tex]l_{B}[/tex]
If A has a greater Young's Modulus than B.
We know that,
The deflection is defined as,
[tex]\delta=\dfrac{Wl}{AE}[/tex]
For material A,
[tex]\delta_{A}=\dfrac{W_{A}l_{A}}{A_{A}E_{A}}[/tex]
[tex]\delta_{A}\propto\dfrac{1}{E_{A}}[/tex]
For material B,
[tex]\delta_{B}=\dfrac{W_{B}l_{B}}{A_{B}E_{B}}[/tex]
[tex]\delta_{B}\propto\dfrac{1}{E_{B}}[/tex]
The deflection is inversely proportional to the young's modulus.
We need to find which cable will stretch the most when loaded
Using formula of deflection
[tex]\dfrac{\delta_{A}}{\delta_{B}}=\dfrac{\dfrac{W_{A}l_{A}}{A_{A}E_{A}}}{\dfrac{W_{B}l_{B}}{A_{B}E_{B}}}[/tex]
Put the value into the formula
[tex]\dfrac{\delta_{A}}{\delta_{B}}=\dfrac{\dfrac{Wl}{AE_{A}}}{\dfrac{Wl}{AE_{B}}}[/tex]
[tex]\dfrac{\delta_{A}}{\delta_{B}}=\dfrac{E_{B}}{E_{A}}[/tex]
So, [tex]\delta_{B}>\delta_{A}[/tex]
Hence, Cable B will more stretch the most.