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Q.

Young’s moduli of the material of wires A and B are in the ratio of 1:4, while its area of cross sections are in the ratio of 1:3. If the same amount of load is applied to both the wires, the amount of elongation produced in the wires A and B will be in the ratio of
(Assume length of wires A and B are same)

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a

12:1

b

36:1

c

1:36

d

1:12

answer is B.

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Detailed Solution

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$\begin{array}{l} \frac{Y_{1}}{Y_{2}} = \frac{1}{4}, \frac{A_{1}}{A_{2}} = \frac{1}{3}; e = \frac{FL}{AY} \\ F_{1} = F_{2} = F, L_{1} = L_{2} = L \\ \frac{e_{1}}{e_{2}} = \frac{A_{2}}{A_{1}} \frac{Y_{2}}{Y_{1}} = 3 \times 4 = 12 \\ e_{1} : e_{2} = 12 : 1 \end{array}$

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