Question

so that work done per unit volume of a wire is half into stress into strain​

Answer 1

Answer:

The stretching force is given by, F=

l

YAΔl

where Y= Young's modulus , A= area of cross-section of the wire, l= actual length of wire and Δl= increase in length.

or F=

l

Y(πr

2

)Δl

As same material so Y becomes constant.

Thus,

F

2

F

1

=

l

1

r

1

2

Δl

1

×

r

2

2

Δl

2

l

2

Given, r

2

=r

1

/2 , l

2

=l

1

/2 and Δl

1

=Δl

2

=1mm

So, F

1

/F

2

=(4

2

/2)=8 .....(1)

The work done in stretching wire by amount Δl is W=(1/2)FΔl

Thus, W

1

/W

2

=F

1

/F

2

or W

2

=(F

2

/F

1

)W

1

=2/8=1/4 as (W

1

=2J)

Explanation:

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