Let a wire be suspended from the ceiling (rigid support) and stretched by a weight $W$ attached at its free en

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 the cross-sectional area $A$ of the wire is:

Accepted Answer

1.  **Definition of Stress:** Longitudinal stress is defined as the internal restoring force ($F$) developed per unit cross-sectional area ($A$) of a body when it is subjected to a deforming force.
    $$	ext{Stress} (\sigma) = \frac{	ext{Restoring Force} (F)}{	ext{Area} (A)}$$
2.  **Force Analysis:** When a weight $W$ is suspended from the free end of the wire, the wire stretches. In a state of equilibrium, the internal restoring force (tension) developed in the wire is equal in magnitude to the external deforming force (the weight $W$).
    $$F = W$$
3.  **Calculation:** Substituting the force into the stress formula:
    $$	ext{Longitudinal Stress} = \frac{W}{A}$$

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