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

The longitudinal stress at any point of cross-sectional area \(A\) in a wire stretched by a weight \(W\) is defined as the force applied per unit area. Stress is given by the formula: 

\[\text{Stress} = \frac{\text{Force}}{\text{Area}} = \frac{W}{A}\]

Here, the force acting on the wire is the weight \(W\), and the area over which this force is distributed is the cross-sectional area \(A\). Therefore, the correct expression for the longitudinal stress in this scenario is \(\frac{W}{A}\).

Answer 2

Stress =\( \frac{IRF}{A}\)

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

(here a cross-sectional area)

Answer 3

The longitudinal stress at any point of cross-sectional area A of the wire is \(\frac{W}{A}\).

Stress is defined as the force acting on a material per unit area. In this case, the force acting on the wire is the weight W, and the cross-sectional area of the wire is A. Therefore, the stress can be calculated as stress = force/area.

In this scenario, the weight W is acting downward, creating tension in the wire. The force is distributed over the cross-sectional area A, so the stress is \(\frac{W}{A}\).