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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Physics
Chapter
Mechanical Properties of Solids

NTA Abhyas 2020 · Physics · Mechanical Properties of Solids

There is some change in length when a 33000N tensile force is...

There is some change in length when a 33000N33000N tensile force is applied on a steel rod of the area of cross-section10−3m2{10}^{- 3}m^{2}. The change of temperature required to produce the same elongation, if the steel rod is heated, is (The modulus of elasticity is 3×1011Nm−23 \times {10}^{11}Nm^{- 2} and the coefficient of linear expansion of steel is 1.1×10−5℃−11.1 \times {10}^{- 5}{℃}^{- 1})

Options

  1. A20°C20 ° C
  2. B15°C15 ° C
  3. C10°C10 ° C
  4. D0°C0 ° C

Correct answer

C. 10°C10 ° C

Step-by-step solution

Modulus of elasticity =ForceArea×l∆l\dfrac{Force}{Area} \times \dfrac{l}{∆ l}

3×1011=3300010−3×l∆l3 \times {10}^{11} = \dfrac{33000}{{10}^{- 3}} \times \dfrac{l}{∆ l}

∆ll=3300010−3×13×1011\dfrac{∆ l}{l} = \dfrac{33000}{{10}^{- 3}} \times \dfrac{1}{3 \times {10}^{11}}

=11×10−5= 11 \times {10}^{- 5}

Change in length, ∆ll=α∆T\dfrac{∆ l}{l} = \alpha ∆ T

11×10−5=1.1×10−5×∆T11 \times {10}^{- 5}=1.1 \times {10}^{- 5} \times ∆ T

⇒∆T=10K⇒∆ T = 10K or& 10°C10 ° C
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