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The breaking stress for a substance is 10 N/ $m^{2}$ . What length of the wire of this substance should be suspended vertically so that the wire breaks under its own weight? (Given: density of material of the wire = 4 × $10^{3}$ kg/ $m^{3}$ and g = 10 m $s^{- 2}$ )

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25 m

15 m

10 m

34 m

answer is C.

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Detailed Solution

Breaking stress = $\frac{M a x i m u m w e i g h t}{A r e a o f c r o s s \sec t i o n}$ . $10^{6} = \frac{a l ρ g}{a} = l ρ g$ $\Rightarrow l = \frac{10^{6}}{ρ g} = \frac{10^{6}}{4 \times 10^{3} \times 10} m = 25 m$

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