Question

A wire is suspended from the ceiling and stretched under the action of a weight F suspended from its other end. The force exerted by the ceiling on it is equal and opposite to the weight
A. Tensile stress at any cross section A of the wire is \[\dfrac{F}{A}\]
B. Tensile stress at any cross section is zero
C. Tensile stress at any cross section A of the wire is \[\dfrac{{2F}}{A}\]
D. Tension at any cross section A of the wire is $2F$

Answer 1

Hint:
In this question, we need to determine the force exerted by the ceiling on it is equal and opposite to the weight. For this we will use the relation between the stress, force, and area of cross-section.

Complete step by step solution:
The wire is stretched under the action of a weight $F$
Since the force exerted by the ceiling on it is equal and opposite to the weight hence we can say the wire is at equilibrium and at equilibrium if the object suspended has the weight $F$, then the tension on the string will be equal to F’. At equilibrium \[F = F'\]

As we know, the tensile stress is the ratio of the magnitude of the force applied on the wire to the cross-section of the wire, this is given by the formula \[S = \dfrac{F}{A}\\ \]
Hence the tensile stress at any cross section A of the wire is \[\dfrac{F}{A}\\ \]

Option A is correct.

Note:
If the force exerted on an object is equal and opposite of its weight, then the object is at equilibrium. Tensile stress is the maximum stress which a material can withstand without being stretched.