High School

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A wire has a cross-sectional area of 4.00 mm\(^2\) and is stretched by 0.100 mm by a certain force. How far will a wire of the same material and length stretch if its cross-sectional area is 8.00 mm\(^2\) and the same force is used to stretch it?

Answer :

Answer: [tex]0.05\ mm[/tex]

Explanation:

Given

Cross-sectional area of wire [tex]A_1=4\ mm^2[/tex]

Extension of wire [tex]\delta l=0.1\ mm[/tex]

Extension in a wire is given by

[tex]\Rightarrow \delta l=\dfrac{FL}{AE}[/tex]

where, [tex]E=\text{Youngs modulus}[/tex]

[tex]\Rightarrow \delta_1=\dfrac{FL}{A_1E}\quad \ldots(i)[/tex]

for same force, length and material

[tex]\Rightarrow \delta_2=\dfrac{FL}{A_2E}\quad \ldots(ii)[/tex]

Divide (i) and (ii)

[tex]\Rightarrow \dfrac{0.1}{\delta_2}=\dfrac{A_2}{A_1}\\\\\Rightarrow \delta_2=0.1\times \dfrac{4}{8}\\\\\Rightarrow \delta_2=0.05\ mm[/tex]

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