Question

A wire stretches by a certain amount under a load if the load and radius are both increase to four times.find the stretch cause in the wire

Answer 1

Answer:

Young's modulus ,

Y=F/πr2×l/Δl or Δl=Fl/πr2Y

When F'=4F and r'=4r , then

Δl'=(4F)l/π(4r)2×Y

∴Δl'/l=14orΔl'=Δl4.

Explanation:

Answer 2

The extension is given by,

$\displaystyle\longrightarrow\sf{\Delta L=\dfrac{FL}{AY}}$

Here, load,

$\displaystyle\longrightarrow\sf{F\mapsto4F}$

And, radius,

$\displaystyle\longrightarrow\sf{r\mapsto 4r}$

$\displaystyle\longrightarrow\sf{r^2\mapsto16r^2}$

Since $\displaystyle\sf{A\propto r^2,}$

$\displaystyle\longrightarrow\sf{A\mapsto16A}$

Then, stretch,

$\displaystyle\longrightarrow\sf{\Delta L\mapsto\dfrac{4FL}{16AY}}$

$\displaystyle\longrightarrow\sf{\Delta L\mapsto\dfrac{1}{4}\cdot\dfrac{FL}{AY}}$

$\displaystyle\longrightarrow\sf{\underline{\underline{\Delta L\mapsto\dfrac{1}{4}\Delta L}}}$

I.e., the stretch becomes one - fourth.