Question

Let a wire be suspended from the ceiling (rigid support) and stretched by a weight W attached at its free end. The longitudinal stress at any point of cross-sectional area A of the wire is:

• A. Zero
• B. \(\frac{2W}{A}\)
• C. \(\frac{W}{A}\)
• D. \(\frac{W}{2A}\)

Answer 1

The Correct Option is C

To determine the longitudinal stress at any point of the wire, we need to understand the fundamental concepts involved in stress and strain in the context of mechanics of materials.

Concept of Stress: When a force is applied perpendicular to the surface of an object, it can cause deformation. In such cases, the internal resistance offered by the body to counteract this deformation is known as stress.

The formula for stress is given by:

\(\text{Stress} = \frac{\text{Force (F)}}{\text{Cross-sectional Area (A)}}\)

For this scenario:

• The force applied is the weight \( W \) of the object hanging from the wire.
• The cross-sectional area \( A \) of the wire is where the stress is being evaluated.

Thus, the longitudinal stress at any point within the cross-sectional area \( A \) of the wire due to the weight \( W \) is:

\(\text{Longitudinal Stress} = \frac{W}{A}\)

This conclusion matches the option "\(\frac{W}{A}\)", making it the correct answer.

Explanation of Incorrect Options:

• Zero: This option is incorrect because there is a force \( W \) applied, resulting in non-zero stress.
• \(\frac{2W}{A}\): This suggests twice the correct value of stress, which does not fit the scenario or formula.
• \(\frac{W}{2A}\): This option implies a smaller value of stress that would be applicable if the force were distributed differently or if geometry affected it differently.

Thus, the correct answer is the third option: \(\frac{W}{A}\).