Question

2- Two materials, A and B, are used to make cables of

Answer 1

Answer:

Cable  B will more stretch the most.

Explanation:

Given that,

Length of material A =$l_{A}$

Length of material B =$l_{B}$

If A has a greater Young's Modulus than B.

We know that,

The deflection is defined as,

$\delta=\dfrac{Wl}{AE}$

For material A,

$\delta_{A}=\dfrac{W_{A}l_{A}}{A_{A}E_{A}}$

$\delta_{A}\propto\dfrac{1}{E_{A}}$

For material B,

$\delta_{B}=\dfrac{W_{B}l_{B}}{A_{B}E_{B}}$

$\delta_{B}\propto\dfrac{1}{E_{B}}$

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

$\dfrac{\delta_{A}}{\delta_{B}}=\dfrac{\dfrac{W_{A}l_{A}}{A_{A}E_{A}}}{\dfrac{W_{B}l_{B}}{A_{B}E_{B}}}$

Put the value into the formula

$\dfrac{\delta_{A}}{\delta_{B}}=\dfrac{\dfrac{Wl}{AE_{A}}}{\dfrac{Wl}{AE_{B}}}$

$\dfrac{\delta_{A}}{\delta_{B}}=\dfrac{E_{B}}{E_{A}}$

So, $\delta_{B}>\delta_{A}$

Hence, Cable  B will more stretch the most.