Question

2 wires a and b are of same material. their lengths are in the ratio of 1:2 and the diameter are in the ratio of 2:1 . if they pulled by same force then increase in length will be in ratio of

Answer 1

Answer:

The increase in the length of two wires in the ratio of 1 : 8

Explanation:

As we know that the extension in length of the wire is given as

$\Delta L = \frac{TL}{AY}$

now the two wires are stretched by same force and made up of same material

So the extension in length in two wires are in ratio given as

$\frac{\Delta L_1}{\Delta L_2} = \frac{\frac{L_1}{\pi r_1^2}}{\frac{L_2}{\pi r_2^2}}$

so we will have

$\frac{\Delta L_1}{\Delta L_2} = \frac{L_1}{L_2} \times (\frac{r_2}{r_1})^2$

$\frac{\Delta L_1}{\Delta L_2} = \frac{1}{2} \times (\frac{1}{2})^2$

$\frac{\Delta L_1}{\Delta L_2} = \frac{1}{8}$

#Learn

Topic : Elasticity

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