Thermal Properties of Matter

JEE Main level, single correct, medium

40 of 126

Question 40 of 126

A steel rail of length 5m5m and area of cross section 40cm240{cm}^{2} is prevented from expanding along its length while the temperature rises by 10∘C10^{\circ}C . If coefficient of linear expansion and Young's modulus of steel are 1.2×10−5K−11.2\times {10}^{-5}{K}^{-1} and 2×1011Nm−22\times {10}^{11}N{m}^{-2} respectively, the force developed in the rail is approximately:

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Answer: (D) 1×105N1\times {10}^{5}N

F=YAαΔtF=YA\alpha \Delta t

⇒F=2×1011×40×10−4×1.2×10−5×10\Rightarrow F=2\times {10}^{11}\times 40\times {10}^{-4}\times 1.2\times {10}^{-5}\times 10

⇒F=9.6×104≈1×105N\Rightarrow F=9.6\times {10}^{4}\approx 1\times {10}^{5}N.

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