Question

12. A wire elongates by mm when a load W is hanged from it. If the wire goes over a

pulley and two weights W, each hung at the two ends, the elongation of the wire will be

(in mm)

a) 2 b) Zero c)

2

d) ​

Answer 1

$\huge\frak{AnswEr :}$

By using the hookes law, we can easily calculate the Elongation.

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So,

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Modules of elasticity is given by :

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$\dag \: \: { \boxed{ \sf{E = \dfrac{W}{A} \times \dfrac{L}{1}}}}$

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where,

• L = original length of the wire

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• A = Area of Cross-section

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Now,

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Elongation will be :

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$\quad\longrightarrow\sf \: \Delta = \dfrac{WL}{E}$

Substituting the values :

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$\quad\longrightarrow\sf \: \Delta = \dfrac{\frac{WL}{E}}{AE}$

$\quad\longrightarrow\sf \: \Delta = \dfrac{WL}{2AE}$

As on either side of the wire, tension is W and length is 1/2.

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$\quad\longrightarrow\sf \: \Delta = \dfrac{1}{2}$

Now,

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$\quad\longrightarrow\sf \: Total \: Elongation = \dfrac{1}{2} + \dfrac{1}{2}$

$\quad\longrightarrow\sf \: Total \: Elongation = \dfrac{2}{2}$

$\quad\longrightarrow\sf \: \large{ \boxed{ \sf{Total \: Elongation = 1}}}$