Question

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A material breaks up under the stress of 20 × 10^5 Nm^-2 . If the density of the material is 2.5× 10^3 kg m^-3 . Calculate the length of wire made of this material which on hanging may break under it's own weight .
(G = 9.8 m s^-2 )
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Answer 1

Solution!!

The breaking stress and density of the material is given. We have to find the length of the wire made of the same material which will break under its own weight on hanging.

Breaking Stress = 20 × 10⁵ Nm^-2

Density (ρ) = 2.5 × 10³ kg m^-3

We know that,

Breaking stress = Breaking force ÷ Area

Further, we know that,

Breaking force = mg

So,

20 × 10⁵ = mg ÷ Area

We can write the mg in terms of density as Vρ

20 × 10⁵ = VρG ÷ Area

Here, V is the volume which can be written as Area × Length

So,

20 × 10⁵ = mg ÷ A = VρG ÷ A = Alρg ÷ A

20 × 10⁵ = lρg

l = (20 × 10⁵) ÷ (ρg)

l = (20 × 10⁵) ÷ (2.5 × 10³ × 9.8)

l = 81.63 m

Hence, the length of the wire is 81.63 m

Answer 2

Answer:

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