Ncert Exercises & Solutions

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 $F/A.$
(b)	Tensile stress at any cross-section is zero.
(c)	Tensile stress at any cross-section $A$ of the wire is $2F/A.$
(d)	Tension at any cross-section $A$ of the wire is $F.$

Choose the correct option from the given ones:
1. (a) and (b) only
2. (a) and (d) only
3. (b) and (c) only
4. (a) and (c) only

Hint: The tension remains the same throughout the length of the wire.

Step: Find the stress developed in the wire.
The force acting on the rod is shown in the figure below;

As shown in the diagram, clearly, the force at each cross-section is

F .

$F.$

The stress developed in the wire is given by;

Stress = \frac{Tension}{Area} = \frac{F}{A}

$\text { Stress }=\frac{\text { Tension }}{\text { Area }}=\frac{F}{A}$
The tension developed in the wire is given by;

\Rightarrow Tension = Applied force = F

$\Rightarrow \text {Tension }=\text { Applied force }=F$
Hence, option (2) is the correct answer.

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