Physics · Thermal Properties of Matter

JEE Main 2025 — 4 April, Evening Shift — Question 53

Consider a rectangular sheet of solid material of length $/=9 \mathrm{~cm}$ and width $d=4 \mathrm{~cm}$ . The coefficient of linear expansion is $\alpha=3.1 \times 10^{-5} \mathrm{~K}^{-1}$ at room temperature and one atmospheric pressure. The mass of sheet $m=0.1 \mathrm{~kg}$ and the specific heat capacity $C_{v}=900 \mathrm{~J} \mathrm{~kg}^{-1} \mathrm{~K}^{-1}$ . If the amount of heat supplied to the material is $8.1 \times 10^{2} \mathrm{~J}$ then change in area of the rectangular sheet is

Option A:
$4.0 \times 10^{-7} \mathrm{~m}^{2}$
Option B:
$2.0 \times 10^{-6} \mathrm{~m}^{2}$
Correct
Option C:
$6.0 \times 10^{-7} \mathrm{~m}^{2}$
Option D:
$3.0 \times 10^{-7} \mathrm{~m}^{2}$

Answer: B

Step-by-step solution

$Q=m c \Delta T$

$8.1 \times 10^{2}=900 \times 0.1 \times \Delta T$

$\Delta T=9 \mathrm{~K}$

$\Delta A=A \cdot 2 \propto \Delta T$

$=36 \times 2 \times 3.1 \times 10^{-5} \times 9 \times 10^{-4}$

$=2 \times 10^{-6} \mathrm{~m}^{2}$

Answer key and solution verified before publishing.

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Exam: JEE Main 2025
Paper: 4 April, Evening Shift
Subject: Physics
Chapter: Thermal Properties of Matter
Topic: Thermal Expansion of Solids and its Applications