A steel wire of length 'L' and area of cross-section 'A' is suspended from rigid support. If '…

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
  1. $\frac{\mathrm{YA}}{\alpha \mathrm{t}}$
  2. $\mathrm{YA} \alpha \mathrm{t}$
  3. $\mathrm{Y} \alpha \mathrm{t}$
  4. $\frac{\mathrm{L} \alpha \mathrm{t}}{\mathrm{Y}}$

Solution

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 $\quad \mathrm{F}=\mathrm{Y} \mathrm{Aa} \Delta \mathrm{T}$

Asked in: MHT CET 2020 (15 Oct Shift 1)

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