First slide

Elastic Modulie

Question

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 $s^{- 2}$ )

Moderate

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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