Question

The coefficient of linear expansion of copper is one and half times that of iron. Identical rods of copper and iron are heated through same temperature range. The ratio of forces developed in them will be (The Young's modulus for copper and iron is the same)

• A. $\frac{2}{3}$
• B. $\frac{4}{9}$
• C. $\frac{9}{4}$
• D. $\frac{3}{2}$

Answer 1

Answer: (D)

$\frac{3}{2}$

If $\alpha$ be coefficient of linear expansion of iron, coefficient of linear expansion of copper $=\frac{\alpha }{2}$.
Thermal force on copper is $F_c=AY\left(\alpha /2\right)\theta$
and thermal force on iron is $F_i=AY\alpha \theta$
$\frac{F_c}{F_i}=\frac{3}{2}$