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  • four wires of the same material are stretched by the same load. Which one of them will elongate most if their dimensions are as follows?  <

four wires of the same material are stretched by the same load. Which one of them will elongate most if their dimensions are as follows?

 

Option: 1

L = 100 cm, r = 1 mm


Option: 2

L = 200 cm, r = 3 mm


Option: 3

L = 300 cm, r = 3 mm


Option: 4

L = 400 cm, r = 4 mm


Answers (1)

best_answer

As,  \Delta L=\frac{FL}{AY}
Because wires of the same material are stretched by the same load. So, fF and Y  will be constant.

\therefore \Delta L\alpha \frac{L}{\pi r^{2}}

    \Delta L_{1}=\frac{100}{\pi \times \left ( 1\times 10^{-3} \right )^{2}}=\frac{100}{\pi \times 10^{-6}}=\frac{100}{\pi }\times 10^{_{6}}

\therefore \Delta L_{2}=\frac{200}{\pi\times \left ( 3\times 10^{-3} \right )^{2}}=\frac{200}{\pi \times 9\times 10^{-6}}=\frac{22.2}{\pi }\times 10^{_{6}}

\therefore \Delta L_{3}=\frac{300}{\pi\times \left ( 3\times 10^{-3} \right )^{2}}=\frac{300}{\pi \times 9\times 10^{-6}}=\frac{33.3}{\pi }\times 10^{_{6}}\therefore \Delta L_{4}=\frac{400}{\pi\times \left ( 4\times 10^{-3} \right )^{2}}=\frac{400}{\pi \times 16\times 10^{-6}}=\frac{25}{\pi }\times 10^{_{6}}

we can see that, L = 100 cm and r = 1 mm will elongate most.

Posted by

Kuldeep Maurya

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