JEE Main 2023 — Physics Thermodynamics

2023integereasy

A thin rod having a length of $1m$ and area of cross-section $3\times {10}^{-6}{m}^{2}$ is suspended vertically from one end. The rod is cooled from $210^{\circ}C$ to $160^{\circ}C$ . After cooling, a mass $M$ is attached at the lower end of the rod such that the length of rod again becomes $1m$ . Young's modulus and coefficient of linear expansion of the rod are $2\times {10}^{11}N{m}^{-2}$ and $2\times {10}^{-5}{K}^{-1}$ , respectively. The value of $M$ is ______ $\mathrm{kg}$ . (Take $g=10m{s}^{-2}$ )

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Held on 31 Jan 2023 · Verified 6 Jul 2026.

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Solution

JEE Main 2023 Physics, Thermal Properties of Matter — solution figure

Let $\Delta l$ be the decease in length of rod due to decease in temperature

Then, $\Delta l=l\alpha \Delta T$ , here, coefficient of linear expansion is $\alpha =2\times {10}^{-5}{K}^{-1}$ and $\Delta T=(483-433)K$ $=50K$

Thus, $\Delta l=1\times 2\times {10}^{-5}\times 50={10}^{-3}m$

Young's modulus is stated as $Y=\frac{\frac{F}{A}}{\frac{\Delta l}{l}}$ , here, $F=Mg$ .

So, $2\times {10}^{11}=\frac{Mg\times 1}{3\times {10}^{-6}\times {10}^{-3}}$

$\Rightarrow Mg=2\times {10}^{11}\times 3\times {10}^{-9}=6\times {10}^{-2}$

Thus, $M=60\mathrm{kg}$

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Solution

JEE Main 2023 Physics, Thermal Properties of Matter — solution figure

Let $\Delta l$ be the decease in length of rod due to decease in temperature

Then, $\Delta l=l\alpha \Delta T$ , here, coefficient of linear expansion is $\alpha =2\times {10}^{-5}{K}^{-1}$ and $\Delta T=(483-433)K$ $=50K$

Thus, $\Delta l=1\times 2\times {10}^{-5}\times 50={10}^{-3}m$

Young's modulus is stated as $Y=\frac{\frac{F}{A}}{\frac{\Delta l}{l}}$ , here, $F=Mg$ .

So, $2\times {10}^{11}=\frac{Mg\times 1}{3\times {10}^{-6}\times {10}^{-3}}$

$\Rightarrow Mg=2\times {10}^{11}\times 3\times {10}^{-9}=6\times {10}^{-2}$

Thus, $M=60\mathrm{kg}$

JEE Main 2023 — Physics Thermodynamics

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JEE Main 2023 — Physics Thermodynamics

Did you get this right?

Solution

Your note

JEE Main Thermodynamics in other years

More JEE Main Thermodynamics questions

Other Physics topics for JEE Main

Mechanics

Electromagnetism

Modern Physics

Optics

Waves & Oscillations

Keep practicing Thermodynamics