First slide

Stress and strain

Question

A substance breaks down under a stress of $10^{5}$ Pa. If the density of the substance is 2 x $10^{3}$ kg/ $m^{3}$ , find the minimum length of the wire made of this substance which will break under its own weight (g = 10 $m / s^{2}$ )

Moderate

A

10 m
B

2.5 m
C

4 m
D

5 m

Solution

Stress at B is maximum, so the wire will break first at B if stress here becomes $10^{5}$ Pa:
$\frac{mg}{A} = 10^{5}$
$\Rightarrow \frac{ALρg}{A} = 10^{5} \Rightarrow L = \frac{10^{5}}{ρg} = 5 m$

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