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Q.

What should be the diameter of a copper wire (y = 1.2 x 10¹⁰ N/m²) of length 5m to produce the same elongation produced by a 5m long aluminium wire (y = 7 x 10¹⁰ N/m²) of diameter 3mm with the same 40kg mass?

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a

1.5mm

b

5mm

c

2.3mm

d

10mm

answer is C.

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Detailed Solution

$\begin{array}{l} e_{1} = e_{2} \\ \frac{Fl}{{πr}_{1}^{2} y_{1}} = \frac{Fl}{{πr}_{2}^{2} y_{2}} \\ r_{1}^{2} y_{1} = r_{2}^{2} y_{2} \end{array}$

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What should be the diameter of a copper wire (y = 1.2 x 1010 N/m2) of length 5m to produce the same elongation produced by a 5m long aluminium wire (y = 7 x 1010 N/m2) of diameter 3mm with the same 40kg mass?