Question

A steel wire of length 4.7 m and cross section 3.0 × 10^-5 m² stretches by the same amount as a copper wire of length 3.5 m and cross section 4.0 × 10 ^ -5 m² under a given load . What's the ratio of young modulus of steel to that of copper?
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Answer 1

Answer:

Young's Modulus for steel, Y

s

,

Y

s

=

A

s

×δl

F×L

s

Young's Modulus for copper, Y

c

,

Y

c

=

A

c

×δl

F×L

c

∴

Y

c

Y

s

=

L

c

×A

s

L

s

×A

c

∵F and δl are constant

∴

Y

c

Y

s

=

3.5×3.0×10

−5

4.7×4.0×10

−5

∴

Y

c

Y

s

=1.79:1

Explanation:

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Answer 2

Solution

Young's Modulus for steel, Ys,

Ys=As×δlF×Ls

Young's Modulus for copper, Yc,

Yc=Ac×δlF×Lc

∴YcYs=Lc×AsLs×Ac ∵F and δl are constant

∴YcYs=3.5×3.0×10−54.7×4.0×10−5

∴YcYs=1.79:1