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  4. A steel rod of length 25 cm has a cross-sectional area of 0.8 cm 2. The force (in N ) required to stretch this rod by the same amount as the expansion produced by heating it through 10° C is coefficient of linear expansion of steel is 10-5 ° C -1. Young's modulus of steel is 2 × 1010 N / m 2.

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Q. A steel rod of length $25\, cm$ has a cross-sectional area of $0.8\, cm ^{2}$. The force (in $N$ ) required to stretch this rod by the same amount as the expansion produced by heating it through $10^{\circ} C$ is coefficient of linear expansion of steel is $10^{-5}{ }^{\circ} C ^{-1}$. Young's modulus of steel is $2 \times 10^{10} N / m ^{2}$.

Thermal Properties of Matter

Solution:

$F = YA \frac{\Delta L }{ L }= YA \alpha \Delta T$
$=2 \times 10^{10} \times\left(0.8 \times 10^{-4}\right) \times 10^{-5} \times 10 N$
$=160 N$