Question

Two steel rods and a copper rod of equal length $l_0$ and equal cross-sectional area are joined rigidly as shown in figure. All the rods are in a state of zero tension at $0{}^{\circ }\text{C}$. The temperature of the system is increased to $30{}^{\circ }\text{C}$. Then:
[coefficient of linear expansion of copper is more than that of steel]

• A. compressive stress acts in steel rods and tensile stress acts in the copper rod.
• B. compressive stress acts in both steel rods and the copper rod.
• C. tensile stress acts in both steel rods and the copper rod.
• D. compressive stress acts in the copper rod and tensile stress acts in the steel rods.

Answer 1

The correct option is D compressive stress acts in the copper rod and tensile stress acts in the steel rods.

We know that, the coefficient of linear expansion of copper is larger than that of steel.
So, the change in natural length of copper is more than that of steel due to rise in temperature. But the rods are rigidly joined with each other, therefore expansions in all rods should be equal.
It means that the stresses produced in the rods have to decrease the length of the copper rod and increase the length of steel rods.
Hence, tensile stress acts in both the steel rods and compressive stress acts in the copper rod.