Mechanical Properties of Solids

Question : 1

Total: 21

A steel wire of length 4.7 m and cross-sectional area 3.0×10–5m2 stretches by the same amount as a copper wire of length 3.5 m and cross- sectional area of 4.0×10–5m2 under a given load. What is the ratio of the Young’s modulus of steel to that of copper?

Solution:

Here, for steel wire,
Area of cross-section, A1=3.0×10−5m2
Stretching, Δl1=Δl (say)
Stretching force on steel, F1=F
For copper wire, length of wire, l2=3.5m
Area of cross-section, A2=4.0×10−5m2
Stretching, Δl2=Δl (given);
Stretching force on copper, F2=F
Let Y1 and Y2 be the Young's modulus of steel and copper wire respectively.

∴Y1=

F1∕A1

Δl1∕l1

F1×l1

A1×Δl1

...(i)

and Y2=

F2×A2

Δl2∕l2

F2×l2

A2×Δl2

F×3.5

4×105×Δl

...(ii)
Dividing (i) by (ii), we get

F×4.7

3×10−5×Δl

4×10−5×Δl

F×3.5

18.8

10.5

=1.79=1.8
⇒Y1:Y2=1.8:1

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