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 α / ° C It is observed that an external compressive force F is ap

Question

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 α / ° 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 ∆ T K Young's modulus, Y for this metal is:

TestHub · Accepted Answer

Since the length of the rod does not change, the increment due to increase in temperature will be balanced by the compression due to applied force.

$Y = \frac{\frac{F}{A}}{\frac{Δ l}{l}} \Rightarrow \frac{Δ l}{l} = \frac{F}{A Y}$

Also $\frac{Δ l}{l} = α Δ T$

$∴ \frac{F}{A Y} = α Δ T$

$Y = \frac{F}{A α Δ T}$

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