Question

A rigid bar of mass 15 kg is supported symmetrically by three wires each 2 m long. Those at each end are of copper and the middle one is of iron. Determine the ratio of their diameters if each is to have the tension.

• A. 12.6 : 2
• B. 1.31 : 1
• C. 4.65 : 3
• D. 2.69 : 4

Hint:

When comparing the tension in wires made of different materials, use the relationship between Young's modulus, cross-sectional area, and elongation to find the required ratios.

Answer 1

The Correct Option is B

The tension in a wire is related to the Young's modulus \( Y \), the cross-sectional area \( A \), and the elongation \( \Delta L \). Since the tension is the same in each wire, we can use the equation: \[ T = Y \frac{A \Delta L}{L} \] Given that the wires are of different materials (copper and iron), the Young's modulus for copper is higher than for iron, and the tension is the same. Therefore, the diameters of the wires must adjust such that their cross-sectional areas and the Young's moduli are balanced to give the same tension. Using the given values and solving for the diameter ratio, we find the ratio of the diameters is \( 1.31 : 1 \). 
Hence, the correct answer is (b).