MHT CET · Physics · Thermal Properties of Matter
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
- A \(\frac{\mathrm{YA}}{\alpha \mathrm{t}}\)
- B \(\mathrm{YA} \alpha \mathrm{t}\)
- C \(\mathrm{Y} \alpha \mathrm{t}\)
- D \(\frac{\mathrm{L} \alpha \mathrm{t}}{\mathrm{Y}}\)
Answer & Solution
Correct Answer
(B) \(\mathrm{YA} \alpha \mathrm{t}\)
Step-by-step Solution
Detailed explanation
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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