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Two wires of different materials, each 2m long and of diameter 2mm are joined in series to form a composite wire. What force will produce a total extension of 0.9 mm.
( $Y_{1} = 2 \times 10^{11} P a & Y_{2} = 6 \times 10^{11} P a$ )

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282.6N

212N

382.6N

319.8N

answer is B.

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Detailed Solution

$e_{1} + e_{2} = 0.9 m m$

$F = Y_{1} A_{1} \frac{e_{1}}{l_{1}} & F = Y_{2} A_{2} \frac{e_{2}}{l_{2}}$

$Y_{1} A_{1} \frac{e_{1}}{l_{1}} = Y_{2} A_{2} \frac{e_{2}}{l_{2}}$

$\frac{e_{1}}{e_{2}} = \frac{Y_{2}}{Y_{1}} = \frac{6 \times 10^{11}}{2 \times 10^{11}} = 3$

$∴ F = Y_{1} A_{1} \frac{e_{1}}{l} = 2 \times 10^{11} \times π {(10^{- 3})}^{2} \times \frac{3}{4} \times \frac{0.9 \times 10^{- 4}}{2}$

= 212 N

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