Question

A wire of length 1 m and radius 1 mm is subjected to a
load. The extension is x. The wire is melted and then
redrawn into a wire of square cross-section of side 2
mm. It's extension under same load is
​

Answer 1

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