A force of 6 × 106 Nm -2 required for breaking a material. The density ρ of the material is 3 × 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 )

Question

A force of 6 × 106 Nm -2 required for breaking a material. The density ρ of the material is 3 × 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) 20 m (B) 200 m (C) 100 m (D) 2000 m

Tardigrade Admin · Accepted Answer

When a wire is pulled it stretches (undergoes strain) upto a certain limit the amount it stretches is proportional to the load divided by the cross-sectional area of the wire.
Stress

= \frac{Force}{Area} = \frac{m g}{A} = \frac{V ρ g}{A} = \frac{L A ρ g}{A}

∴

Stress

= L ρ g

Given, stress

= 6 \times 1 0^{6} N m^{- 2}

ρ = 3 \times 1 0^{3} k g m^{- 3}

g = 10 m s^{- 2}

L = \frac{stress}{ρ g}

= \frac{6 \times 1 0 ^{6}}{3 \times 1 0 ^{3} \times 10}

= 2 \times 1 0^{2} = 200 m

Q. A force of 6×106Nm−2 required for breaking a material. The density ρ of the material is 3×103kgm−3. If the wire is to break under its own weight, the length of the wire made of that material should be (take g=10ms−2 )

20 m

200 m

100 m

2000 m

Q. A force of $6 \times 1 0^{6} N m^{- 2}$ required for breaking a material. The density $ρ$ of the material is $3 \times 1 0^{3} k g m^{- 3}$ . If the wire is to break under its own weight, the length of the wire made of that material should be (take $g = 10 m s^{- 2}$ )