A substance breaks down by a stress of 10^6 N/m2 . If the density of the material of the wire is 3 × 10^3 kg/m3 , then the length of the wire of the substance which will break under its own weight when suspended vertically, is

Q: A substance breaks down by a stress of 106 N/m2 . If the density of the material of the wire is 3 × 103 kg/m3 , then the length of the wire of the substance which will break under its own weight when suspended vertically, is

(a) 66.6 m

(b) 60.0 m

(c) 33.3 m

(d) 30.0 m

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Ans: (c)
Sol: $Stress = \frac{M g}{A}$

$Stress = \frac{(A L \rho ) g}{A}$ (Since , Mass = Area x Length x Density )

$ Stress = L \rho g $

$L = \frac{Stress }{\rho g}$

$L = \frac{10^6 }{3 \times 10^3 \times 10}$

L = 33.3 m