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 $\alpha / {^{\circ}C}$. 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 $\Delta T K$. Young's modulus, $Y$, for this metal is :

• A. $\frac{F}{2A\alpha\Delta T}$
• B. $\frac{F}{A\alpha \left(\Delta T - 273\right)}$
• C. $\frac{F}{A\alpha \Delta T}$
• D. $\frac{2F}{A\alpha \Delta T}$

Answer 1

Answer: (C)

$\frac{F}{A\alpha \Delta T}$

Answer 2

Young's modulus $y = \frac{\text{Stress}}{\text{Strain}}$
$=\frac{F/A}{\left(\Delta \ell/\ell\right)}$
$= \frac{F}{A\left(\alpha \Delta T\right)}$