A metal rod having coefficient of linear expansion $2 imes 10^{-5} /{ }^{\circ} \mathrm{C}$ is 0.75 m long at $45^{\circ} \mathrm{C}$. When the temperature rises to $65^{\circ} \mathrm{C}$, the increase in length of the rod will be

Question

A metal rod having coefficient of linear expansion $2 	imes 10^{-5} /{ }^{\circ} \mathrm{C}$ is 0.75 m long at $45^{\circ} \mathrm{C}$. When the temperature rises to $65^{\circ} \mathrm{C}$, the increase in length of the rod will be

Aicharya · Accepted Answer

$\begin{aligned} \alpha & =\frac{\mathrm{d} l}{l 	imes \mathrm{dt}} \ \mathrm{d} l & =\alpha 	imes l 	imes \mathrm{dt} \ & =2 	imes 10^{-5} 	imes 0.75 	imes\left(65^{\circ}-45^{\circ}ight) \ & =0.3 	imes 10^{-3} \mathrm{~m}=0.30 \mathrm{~mm}\end{aligned}$

A metal rod having coefficient of linear expansion $2 \times 10^{-5} /{ }^{\circ} \mathrm{C}$ is 0.75 m long…

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