Question

A wire of length 1m 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 it's extension under the same load

Answer 1

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11th

Physics

Mechanical Properties of Solids

Stress and Strain

A wire of length 1\ m and...

PHYSICS

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 the extension under the same load?

December 20, 2019

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Ankit Purohit

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ANSWER

Given that,

Length l=1m

Radius r=1mm

Extension =x

Cross section area of wireA=πr

2

=πmm

2

The volume of the wire V=Al=πmm

3

Now, after melting

The length of the wire l=

A

V

=πmm

Now, we know that

Stress=strain∗constant

For case first,

A

F

=stress

l

Δl

=strain

Now,

A×Δl

F×l

=constant

Now, we have

A

1

×Δl

1

F

1

×l

1

=

A

2

×Δl

2

F

2

×l

2

x×π

1

=

Δl

2

π

Δl

2

=π

2

x

Hence, the extension under the same load is π

2

x