Mechanical Properties of Solids

JEE Main level, single correct, medium

78 of 118

Question 78 of 118

A copper wire of length 1.0 m1.0 \mathrm{~m} and a steel wire of length 0.5 m0.5 \mathrm{~m} having equal cross-sectional areas are joined end to end. The composite wire is stretched by a certain load which stretches the copper wire by 1 mm1 \mathrm{~mm}. If the Young's modulii of copper and steel are respectively 1.0×10111.0 \times 10^{11} Nm−2\mathrm{Nm}^{-2} and 2.0×1011Nm−22.0 \times 10^{11} \mathrm{Nm}^{-2}, the total extension of the composite wire is :

Show answer and solution

Answer: (D) 1.25 mm1.25 \mathrm{~mm}

Yc×(ΔLc/Lc)=Ys×(ΔLs/Ls)\mathrm{Y}_{\mathrm{c}} \times\left(\Delta \mathrm{L}_{\mathrm{c}} / \mathrm{L}_{\mathrm{c}}\right)=\mathrm{Y}_{\mathrm{s}} \times\left(\Delta \mathrm{L}_{\mathrm{s}} / \mathrm{L}_{\mathrm{s}}\right)
⇒1×1011×(1×10−31)=2×1011×(ΔLs0.5)\Rightarrow 1 \times 10^{11} \times\left(\frac{1 \times 10^{-3}}{1}\right)=2 \times 10^{11} \times\left(\frac{\Delta \mathrm{L}_{\mathrm{s}}}{0.5}\right)

∴ΔLs=0.5×10−32=0.25 mm\therefore \Delta \mathrm{L}_{\mathrm{s}}=\frac{0.5 \times 10^{-3}}{2}=0.25 \mathrm{~mm}
Therefore, total extension of the composite
 wire =ΔLc+ΔLs=1 mm+0.25 m=1.25 m\begin{aligned} & \text { wire }=\Delta \mathrm{L}_{\mathrm{c}}+\Delta \mathrm{L}_{\mathrm{s}} \\ & =1 \mathrm{~mm}+0.25 \mathrm{~m}=1.25 \mathrm{~m} \end{aligned}

JEE Main question paper PDF

Open a shift to read the full paper on this page, or download it.

JEE Main 2025 Apr 2 Shift 1 question paper

Open Download PDF

Opening paper…

Explain it as a whiteboard videoStep-by-step, in Hinglish or English. Your first video needs no login.Solved it on paper but got it wrong?Upload a photo of your working. Mistake Doctor marks the exact line that broke.
See it move: Elasticity: stress, strain and Young’s modulus simulationDrag the sliders and watch the numbers in this question change.

More Physics practice

JEE Main Physics practice question on Mechanical Properties of Solids (Young's Modulus and Breaking Stres), with the answer and a step-by-step solution. Scan a question from your own book or paper to get a whiteboard video.