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Question

# There is some change in length when a 33,000 N tensile force is applied on a steel rod of area of cross-section 10−3 m2. The change of temperature required to produce the same elongation, if the steel rod is heated, is - [Take modulus of elasticity Y=3×1011N/m2 and the coefficient of linear expansion of steel is α=1.1×10−5/∘C]

A
20C
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B
15C
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C
10C
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D
0C
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Solution

## The correct option is C 10∘CFrom the definition, Modulus of elasticity =ForceArea×lΔl ....(1) Given, Tensile force (F)=33,000 N Area of cross-secton (A)=10−3 m2 Modulus of elasticity Y=3×1011N/m2 and Coefficient of linear expansion of steel is α=1.1×10−5/∘C Using the given data in (1), we get 3×1011=33,00010−3×lΔl ⇒Δll=33,00010−3×13×1011=11×10−5 .....(2) We know that, change in length of the wire due to heating is, Δl=l(αΔT) ....(3) From (2) and (3), αΔT=11×10−5 ⇒11×10−5=1.1×10−5×ΔT ⇒ΔT=10 K or 10∘C Thus, option (c) is the correct answer.

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