Verified Solution • 2025–26 Session moderate

QJEEM19Phb9d4: JEE Main 2019 Physics - Class 11 JEEM19Phb9d4 Solution: A rod, of length L at room temperature and uniform area of…

A rod, of length L at room temperature and uniform area of cross section A, is made of a metal having coefficient of linear expansion α\alpha /oC. It is observed that an external compressive force F, is applied on each of its ends, prevents any change in the length of the rod, when its temperature rises by Δ\Delta TK. Young's modulus, Y, for this metal is :

Multiple Choice Options

  • A FAαΔT{F \over {A\alpha \Delta T}}
  • B FAα(ΔT−273){F \over {A\alpha (\Delta T - 273)}}
  • C F2AαΔT{F \over {2A\alpha \Delta T}}
  • D 2FAαΔT{{2F} \over {A\alpha \Delta T}}

Step-by-Step Verified Solution

We know,

Young's Modulus, Y = StressStrain{{Stress} \over {Strain}}

Stress = FA{F \over A}

Strain = Δll{{\Delta l} \over l}

∴\therefore   Y = FAΔll{{{F \over A}} \over {{{\Delta l} \over l}}}

We also know,

ll f = ll i (1 + α\alpha Δ\Delta T)

⇒\Rightarrow     ll f = ll i + ll i α\alpha Δ\Delta T

⇒\Rightarrow     lf−lili{{{l_f} - {l_i}} \over {{l_i}}} = α\alpha ΔT\Delta T

⇒\Rightarrow     Δlli{{\Delta l} \over {{l_i}}} = α\alpha Δ\Delta T

∴\therefore    y = FAαΔT{{{F \over A}} \over {\alpha \Delta T}}

= FAαΔT{F \over {A\alpha \Delta T}}

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