Ncert Exercises & Solutions

Q.19 A wire of length L and radius r is clamped rigidly at one end. When the other end of the wire is pulled by a force f, its length increases by l. Another wire of the same material of length 2L and radius 2r is pulled by a force 2f. Find the increase in length of this wire.

Hint: For the same material, Young's modulus will be the same.

Step 1: Find Young's modulus for both the wires.

The situation is shown in the diagram.

Now, young's modulus (Y)

= \frac{f}{A} \times \frac{L}{l}

For the first wire,

Y = \frac{f}{{πr}^{2}} \times \frac{L}{l}

...(i)

For the second wire,

Y = \frac{2 f}{π {(2 r)}^{2}} \times \frac{2 L}{l'}

= \frac{f}{{πr}^{2}} \times \frac{L}{l'}

...(ii)

Step 2: Find the increase in the length of the second wire.

From Eqs. (i) and (ii),

\frac{f}{{πr}^{2}} \times \frac{L}{l} = \frac{f}{{πr}^{2}} \times \frac{L}{l'}

l = l'

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