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A rod of length L at room themarature and Uniform area of Cross section A, is made of a metal having Coefficient of linear expansion $\frac{α}{^{0} c}$ . it is observed that an external compressive force F is applied on each of its ends, prevents any change in the length of the rod, When its temperature rises by $Δ T K$ .Young’s modulus Y, for this metal is

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$\frac{F}{2 A α Δ T}$

$\frac{F}{A α Δ T}$

$\frac{F}{A α (Δ T - 273)}$

$\frac{2 F}{A α Δ T}$

answer is B.

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Detailed Solution

If a rod of length l and coefficient of linear

expansion $α /^{0} c$ , than with rise in
temperature by $Δ T K$ its change in length is
$Δ L = L α Δ T$

$\frac{Δ L}{L} = α Δ T$ $[\begin{array}{l} ∵ Y = \frac{Stress}{Strain} = \frac{\frac{F}{A}}{\frac{Δ L}{L}} \\ \frac{Δ L}{L} = \frac{F}{Y A} \end{array}]$

$\frac{F}{Y A} = α Δ T$

$Y = \frac{F}{A α Δ T}$

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