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Physics Question on Stress and Strain

A load of 1 kg1\, kg weight is a attached to one end of a steel wire of area of cross-section 3 mm2 3 \, mm^2 and Young's modulus 1011 N/m210^{11} \, N/m^2. The other end is suspended vertically from a hook on a wall, then the load is pulled horizontally and released. When the load passes through its lowest position the fractional change in length is (g=10 m/s2)(g = 10 \, m/s^2)

A

0.3×10−40.3 \times 10^{-4}

B

0.3×10−30.3 \times 10^{-3}

C

0.3×1030.3 \times 10^{3}

D

0.3×1040.3 \times 10^{4}

Answer

0.3×10−40.3 \times 10^{-4}

Explanation

Solution

Y=mglAΔlY=\frac{m g l}{A \Delta l}
⇒Δll=mgAY\Rightarrow \frac{\Delta l}{l}=\frac{m g}{A Y}
∴Δll=1×103×10−6×1011\therefore \frac{\Delta l}{l}=\frac{1 \times 10}{3 \times 10^{-6} \times 10^{11}}
=0.3×10−4=0.3 \times 10^{-4}