Question

A composite rod consists of a steel rod of length $25cm$ and area $2A$ and a copper rod of length $50cm$ and area $A$. The composite rod is subjected to an axial load $F$. If the Young's modulii of steel and copper are in the ration $2:1$, then

• A. The extension produced in copper rod will be more
• B. The extension in copper and steel parts will be in the ratio $1:2$
• C. The stress applied to copper rod will be more
• D. No extension will be produced in the steel rod

Answer 1

Answer: (A), (B), (C)

The correct options are
A The extension produced in copper rod will be more
B The extension in copper and steel parts will be in the ratio $1:2$
C The stress applied to copper rod will be more

$Stress=\frac{Force}{Area}$. Since force applied on both materials is same, but area of steel is more, so stress for copper will be more.

$\Delta l=\frac{FL}{AY}$

Force is same for both.

Thus, $Extension,\Delta l\propto \frac{l}{AY}$

Thus$\frac{{\Delta l}_{Steel}}{{\Delta l}_{Copper}}\propto \frac{{\left(\frac{l}{AY}\right)}_{Steel}}{{\left(\frac{l}{AY}\right)}_{Copper}}$

=$\frac{\left(\frac{25}{2A.2Y}\right)}{\left(\frac{50}{AY}\right)}=1:8$