Question

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A wire of length 1 m and radius
1mm is subjected to a load.The extension is 'x'. The wire is melted
and then drawn into a wire of square cross section of side 1mm.
What is its extension under the same load ❔❔
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Answer 1

Answer:

$\huge\bf{GIVEN\:}$

• Length of Wire = 1 m
• Square Cross Section = 1mm

$\bold\blue{Solution}$

$\bold\orange{Young\:Module\:-\:?}$

$\bf = \frac{Stress}{Strain}$

$⟶ {r\:= \frac{ \frac{L}{π(1)^2} }{ {X}{1} }$

Where L is the Load,

$⟶ {r\:= \frac{L}{πX}}$

r is the Properly wire,

${r\:= \frac{ \frac{L}{(1)^2}}{{X'}{l'}}$

As volume will remain same, (1) [π(1)²] =

l (1)²

So,

$⟶ \frac{L}{πX}}$

$⟶ \frac{ \frac{L}{X'}}{x}}$

$⟶{X'}$

$⟶ {π^2X}$