A rod of length \(L\) at room temperature and uniform area of cross section \(A\), is made of a metal having coefficient of linear expansion \(\alpha {/^o}C\). 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 it temperature rises by \(\Delta \,TK\). Young’s modulus, \(Y\), for this metal is

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Correct Answer

(A) \(\frac{F}{{A\alpha \,\Delta T}}\)

Step-by-step Solution

Detailed explanation

\(\Delta L = L \propto \Delta T\)

\(Strain = \frac{{\Delta L}}{L} = \propto \Delta T\,\,;\,\,Y = \frac{F}{{A \propto \Delta T}}\)

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