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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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212 N

319.8 N

$282.6 N$

382.6 N

answer is B.

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Detailed Solution

$Y_{n e t} = \frac{2 Y_{1} Y_{2}}{Y_{1} + Y_{2}} = \frac{2 \times 2 \times 10^{11} \times 6 \times 10^{11}}{2 \times 10^{11} + 6 \times 10^{11}} = 3 \times 10^{11}$

$F = \frac{Y A e}{L} = \frac{3 \times 10^{11} \times 3.14 \times {(10^{- 3})}^{2} \times 0.9 \times 10^{- 3}}{4} = 212 N$

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