Step 1: Use the Formula for Elongation
The elongation of a wire is given by:
$$ \Delta L = \frac{\sigma L}{Y} $$
\(\Delta L\) = Elongation of the wire
\(\sigma\) = Stress (Elastic limit)
L = Length of the wire
Y = Young’s modulus
Step 2: Substitute the Given Values
Given:
\(\sigma = 8 \times 10^8 \text{ N/m}^2\)
\(L = 1 \text{ m}\)
\(Y = 2 \times 10^{11} \text{ N/m}^2\)
Substituting these values into the equation:
$$ \Delta L = \frac{(8 \times 10^8) \times 1}{2 \times 10^{11}} $$
Step 3: Convert the Result
Solving the equation:
$$ \Delta L = 4 \times 10^{-3} \text{ m} $$
Converting to millimeters:
$$ \Delta L = 4 \text{ mm} $$
Conclusion
The elongation of the wire is 4 mm.
List I | List II | ||
---|---|---|---|
A | Mesozoic Era | I | Lower invertebrates |
B | Proterozoic Era | II | Fish & Amphibia |
C | Cenozoic Era | III | Birds & Reptiles |
D | Paleozoic Era | IV | Mammals |