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Physics Question on mechanical properties of solids

A steel wire having a radius of 2.0 mm2.0\, mm, carrying a load of 4 kg4 \,kg, is hanging from a ceiling. Given that g=3.1  π  ms−2g = 3.1 \; \pi \; ms^{-2}, what will be the tensile stress that would be developed in the wire ?

A

4.8×106  Nm−2 4.8 \times 10^6 \; Nm^{-2}

B

5.2×106  Nm−2 5.2 \times 10^6 \; Nm^{-2}

C

6.2×106  Nm−2 6.2 \times 10^6 \; Nm^{-2}

D

3.1×106  Nm−23.1 \times 10^6 \; Nm^{-2}

Answer

3.1×106  Nm−23.1 \times 10^6 \; Nm^{-2}

Explanation

Solution

Tensile stresss in wire will be
=Tensile   force  Cross    section   Area= \frac{ \text{Tensile } \; \text{force }}{ \text{ Cross } \; \text{ section} \; \text{ Area}}
=mgπR2=4×3.1ππ×4×10−6Nm−2=3.1×106Nm−2= \frac{mg}{\pi R^{2}} = \frac{4\times3. 1 \pi}{\pi \times4 \times10^{-6}} Nm^{-2} = 3.1 \times10^{6} Nm^{-2}