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A steel wire of length 'L' and area of cross-section 'A' is suspended from rigid
support. If ' $\mathrm{Y}^{\prime}$ is the Young's modulus of material of the wire and ' $\alpha$ ' is the coefficient of linear expansion, then the increase in tension when temperature
falls by $t^{\circ} \mathrm{C}$ is
Options:
support. If ' $\mathrm{Y}^{\prime}$ is the Young's modulus of material of the wire and ' $\alpha$ ' is the coefficient of linear expansion, then the increase in tension when temperature
falls by $t^{\circ} \mathrm{C}$ is
Solution:
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Verified Answer
The correct answer is:
$\mathrm{YA} \alpha \mathrm{t}$
Let $\mathrm{F}$ be tension developed in the wire.
$\therefore \quad \mathrm{Y}=\frac{\mathrm{F} / \mathrm{A}}{\Delta \mathrm{L} / \mathrm{L}}$
As $\Delta \mathrm{L}=\mathrm{La} \Delta \mathrm{T}$
$\therefore \quad \mathrm{Y}=\frac{\mathrm{F}}{\mathrm{Aa} \Delta \mathrm{T}}$ or $\quad \mathrm{F}=\mathrm{Y} \mathrm{Aa} \Delta \mathrm{T}$
$\therefore \quad \mathrm{Y}=\frac{\mathrm{F} / \mathrm{A}}{\Delta \mathrm{L} / \mathrm{L}}$
As $\Delta \mathrm{L}=\mathrm{La} \Delta \mathrm{T}$
$\therefore \quad \mathrm{Y}=\frac{\mathrm{F}}{\mathrm{Aa} \Delta \mathrm{T}}$ or $\quad \mathrm{F}=\mathrm{Y} \mathrm{Aa} \Delta \mathrm{T}$
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