Question

For steel, the breaking stress is 6 x10^6N/m² and the
density is 8x10^3 kg/m? The maximum length of steel
wire, which can be suspended without breaking under
its own weight is (g = 10 m/s^2)​

Answer 1

The maximum length of the steel wire which can be suspended without breaking under its own weight is 75 m

Explanation:

If the cross sectional area of the steel rod is A and the length is L then the Volume of the steel rod will be LA

Mass of the steel rod will be

Mass = Volume × Density

$M=LA\times 8\times 10^3$

We know that

$\text{Stress}=\frac{\text{Force}}{\text{Area}}$

Therefore,

$6\times 10^6=\frac{Mg}{A}$

$\implies 6\times 10^6=\frac{LA\times 8\times 10^3\times 10}{A}$

$\implies 6\times 10^6=L\times 8\times 10^4$

$\implies L=\frac{6\times 10^6}{8\times 10^4}$

$\implies L=\frac{6\times 100}{8}$

$\implies L=3\times 25$

$\implies L=75$ m

Therefore, the maximum length of the steel wire which can be suspended without breaking under its own weight is 75 m

Hope this answer is helpful.

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