A stress of 6 X 106 Nm-2 required for breaking a material. The density ρ of the material is 3 X 103 kg m-3. If the wire is to break under its own weight, the length of the wire made of that material should be (Take, g = 10 ms-2)

A stress of 6 X 10⁶ N $m^{- 2}$ required for breaking a material. The density $ρ$ of the material is 3 X 10³ kg $m^{- 3}$ . If the wire is to break under its own weight, the length of the wire made of that material should be
(Take, g = 10 m $s^{- 2}$ )

A
20 m
B
200 m
C
100 m
D
2000 m

Solution:

The minimum stress after which the wire breaks, i.e.

$Stress = \frac{Force}{Area} = \frac{m g}{A}$

$= \frac{V ρ g}{A} = \frac{L A ρ g}{A} = L ρ g$

Given, stress $= 6 \times 10^{6} {Nm}^{- 2}$

$ρ = 3 \times 10^{3} {kgm}^{- 3} and g = 10 {ms}^{- 2}$

$\Rightarrow L = \frac{Stress}{ρ g} = \frac{6 \times 10^{6}}{3 \times 10^{3} \times 10}$

$= 2 \times 10^{2} = 200 m$

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