Verified Solution • 2025–26 Session moderate

QJEEM17Ph55ae: JEE Main 2017 Physics - Class 11 JEEM17Ph55ae Solution: A steel rail of length 5 m and area of cross section 40cm 2 is…

A steel rail of length 5 m and area of cross section 40cm2 is prevented from expanding along its length while the temperature rises by 10oC. If coefficient of linear expansion and Young’s modulus of steel are 1.2×10−5 K−1 and 2×1011 Nm−2 respectively, the force developed in the rail is approximately :

Multiple Choice Options

  • A 2 ×\times 107 N
  • B 1 ×\times 105 N
  • C 2 ×\times 109 N
  • D 3 ×\times 10 −- 5 N

Step-by-Step Verified Solution

Young's modulus (Y) = FAΔLL{{{F \over A}} \over {{{\Delta L} \over L}}}

as   ΔLL{{{\Delta L} \over L}} = α\alpha Δ\Delta θ\theta

∴   \therefore\,\,\, Y = FAαΔθ{{F \over {A\alpha \Delta \theta }}}

⇒\Rightarrow    \,\,\, F = YA α\alpha Δ\Delta θ\theta

= 2 ×\times 1011 ×\times 40 ×\times 10 −- 4 ×\times 1.2 ×\times 10 −- 5 ×\times 10

= 9.6 ×\times 104 N

≃\simeq 1 ×\times 105 N

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