First slide

Stress and strain

Question

A stress of $10^{6} {Nm}^{- 2}$ is required for breaking a material. If the density of the material is $3 \times 10^{3} {kgm}^{- 3},$ then what should be the length of the wire made of this material, so that it breaks under its own weight?

Moderate

A

10 m
B

5 m
C

33.3 m
D

66.6 m

Solution

Maximum breaking stress
$\begin{array}{l} = \frac{F}{A} = \frac{mg}{A} = \frac{(Alρ) g}{A} = S_{max} \\ ∴ I_{max} = \frac{S_{max}}{ρg} = \frac{10^{6}}{(3 \times 10^{3}) (10)} = 33.33 m \end{array}$

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