Question

A copper wire and a steel wire of the same diameter and length are joined end to end and a force is applied which stretches their combined length by 1cm. Then the two wires will have.
A) the same stress and strain.
B) the same stress but different strains.
C) the same strain but different stresses.
D) different stresses and strains.

Answer 1

Stress is the ratio of applied force to the area of cross section and strain is the ratio of change in length due to applied load to the original length. The formula of stress and strain can help to solve this problem.

Formula used:
The change in length of the wire is given by $\Delta l = \dfrac{{F \cdot l}}{{A \cdot E}}$ where $F$ is applied force, $l$ is length, $A$ is area of cross section, $\Delta l$ is change in length and $E$ is young’s modulus of elasticity.

Complete step by step answer:
As the stress is defined as the ratio of force and area of cross section and here there are two wires of different materials one is copper and other is steel which means that the young’s modulus of these materials will be different as the young’s modulus depends upon the material but as the diameter of area of both the wires i.e. copper and steel is same therefore the cross section area would be same and as the stress is the ratio of force and cross section and the applied load will be same for both the wires which means that the stress will be same.
As the formula of change in length is $\Delta l = \dfrac{{F \cdot l}}{{A \cdot E}}$, where $F$ is the force applied $l$ is the original length $A$ is the area of cross section and $E$ is the young’s modulus of elasticity.
So the change in length for both of the wires will be different as the young’s modulus is different material is never the same. So wires will have the same stress but different strains.

Therefore, the correct answer is option B.

Note:
It is advisable to remember the formula of the change in length as sometimes direct numerical questions are asked also it helps in solving such types of problems. The young’s modulus is defined as the ratio of stress and strain.