A metallic rod having area of cross section $A$, Young’s modulus $Y$, coefficient of linear expansion $\alpha $ and length $L$ tied with two strong pillars. If the rod is heated through a temperature $t\,^oC$ then how much force is produced in rod ?
A metallic rod having area of cross section $A$, Young’s modulus $Y$, coefficient of linear expansion $\alpha $ and length $L$ tied with two strong pillars. If the rod is heated through a temperature $t\,^oC$ then how much force is produced in rod ?
$\mathrm{Y}=\frac{\mathrm{F} / \mathrm{A}}{l / \mathrm{L}}=\frac{\mathrm{FL}}{\mathrm{Al}}$ where $l=\mathrm{L} \propto \Delta t$
$\therefore \mathrm{Y}=\frac{\mathrm{FL}}{\mathrm{AL} \propto \Delta t}=\frac{\mathrm{F}}{\mathrm{A} \propto \Delta t}$
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