If the ratio of diameters, lengths and Young's modulus of steel and… | NEET 2013

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Wire Combinations & Special Cases

If the ratio of diameters, lengths and Young's modulus of steel and copper wires shown in the figure are p, q and s respectively, then the corresponding ratio of increase in their lengths would be

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Answer: (b)

Tension in steel (holds both blocks) $= 7mg$ ; tension in copper $= 5mg$ .
$\Delta l = \frac{TL}{(\pi d^2/4)Y}$ , so $\frac{\Delta l_s}{\Delta l_c} = \frac{T_s}{T_c} \cdot \frac{L_s}{L_c} \cdot \frac{d_c^2}{d_s^2} \cdot \frac{Y_c}{Y_s}$
$= \frac{7}{5} \cdot q \cdot \frac{1}{p^2} \cdot \frac{1}{s} = \frac{7q}{5sp^2}$
So the answer is (b).

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