Ncert Exercises & Solutions

A copper and a steel wire of the same diameter are connected end to end. A deforming force \(F\) is applied to this composite wire which causes a total elongation of \(1\) cm. The two wires will have:

a.	the same stress
b.	different stress
c.	the same strain
d.	different strain

Choose the correct option:

1.	(a, b)
2.	(a, d)
3.	(b, c)
4.	(c, d)

(2) Hint: The tension or compression in the wires will be the same.

Step 1: Find the stress in both the wires.

Consider the diagram where a deforming force F is applied to the combination.

For steel wire,

Y_{steel} = \frac{Stress}{Strain} = \frac{F / A}{{(Strain)}_{steel}}

For copper wire,

Y_{copper} = \frac{Stress}{Strain} = \frac{F / A}{{(Strain)}_{copper}}

where F is tension in each wire and A is the cross-section area of each wire.

As F and A are the same for both the wires, hence, stress will be the same for both the wires.

Step 2: Find the strain in the two wires.

{(Strain)}_{steel} = \frac{Stress}{Y_{steel}}

{(Strain)}_{copper} = \frac{Stress}{Y_{copper}}

Y_{steel} \neq Y_{copper}

Hence, the two wires will have different strain.

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