Question

When a tension of \(F_1\) is applied on a metal wire its length is \(L_1\), if the tension is \(F_2\), length becomes \(L_2\). Then the original length of the wire is:

• A. 2\( \frac{F_2 - F_1}{F_1 + F_2}L_2 \)
• B. \( \frac{F_2 L_1 - F_1 L_2}{F_2 - F_1} \)
• C. \( F_1 L_1 - F_2 L_2 \)
• D. \( (F_1 - F_2) L_2 \)

Hint:

In problems involving elasticity, the original length can often be deduced by considering changes under different forces and applying principles from material science.

Answer 1

The Correct Option is B

Step 1: Apply the principle of superposition of forces. Assuming linear elasticity, the change in length due to each force can be superimposed. Step 2: Calculate the original length \(L\). Using the relationship between force and elongation: \[ \Delta L = \frac{F \cdot L}{EA} \] Solving for \(L\) with the known conditions gives: \[ L = \frac{F_2 L_1 - F_1 L_2}{F_2 - F_1} \]