KCET · Physics · Mechanical Properties of Solids
The following four wires of length \(L\) and radius \(r\) are made of the same material. Which of these will have the largest extension, when the same tension is applied?
- A \(L=100 \mathrm{~cm}, r=0.2 \mathrm{~mm}\)
- B \(L=200 \mathrm{~cm}, r=0.4 \mathrm{~mm}\)
- C \(L=300 \mathrm{~cm}, r=0.6 \mathrm{~mm}\)
- D \(L=400 \mathrm{~cm}, r=0.8 \mathrm{~mm}\)
Answer & Solution
Correct Answer
(A) \(L=100 \mathrm{~cm}, r=0.2 \mathrm{~mm}\)
Step-by-step Solution
Detailed explanation
Extension of wire \(e=\frac{F L}{A Y}\)
\(e=\frac{F L}{\pi r^{2} Y}\)
\(F\) and \(Y\) are same for all wires
\(\therefore\) \(e \propto \frac{L}{r^{2}} \)
\(e_{a}=\frac{1000}{0.2 \times 0.2}=25000 \)
\(e_{b}=\frac{2000}{0.4 \times 0.4}=12500 \)
\(e_{c}=\frac{3000}{0.6 \times 0.6}=8333.4 \)
\(e_{d}=\frac{4000}{0.8 \times 0.8}=6250\)
We can see that, first wire have the largest extension.
\(e=\frac{F L}{\pi r^{2} Y}\)
\(F\) and \(Y\) are same for all wires
\(\therefore\) \(e \propto \frac{L}{r^{2}} \)
\(e_{a}=\frac{1000}{0.2 \times 0.2}=25000 \)
\(e_{b}=\frac{2000}{0.4 \times 0.4}=12500 \)
\(e_{c}=\frac{3000}{0.6 \times 0.6}=8333.4 \)
\(e_{d}=\frac{4000}{0.8 \times 0.8}=6250\)
We can see that, first wire have the largest extension.
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