Question

A rod, of length $L$ at room temperature and uniform area of cross section $A$, is made of a metal having a coefficient of linear expansion ${}^{o}C$. 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 its temperature rises by $\Delta TK$. Young's modulus, $Y$, for this metal is :

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

Answer 1

Answer: (C)

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

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