The two wires A and B of equal cross-section but of different materials are joined together

Question

The two wires A and B of equal cross-section but of different materials are joined together. The ratio of Young’s modulus of wire A and wire B is 20/11. When the joined wire is kept under certain tension the elongations in the wires A and B are equal. If the length of wire A is 2.2 m, then the length of wire B is ______ m. [2026]

Smart Achievers · Accepted Answer

(3)

$Given: \frac{Y_{A}}{Y_{B}} = \frac{20}{11}, A_{1} = A_{2}, F_{1} = F_{2}$

$Δ L_{1} = Δ L_{2} \Rightarrow \frac{F L_{A}}{A Y_{A}} = \frac{F L_{B}}{A Y_{B}}$

$L_{B} = \frac{Y_{B}}{Y_{A}} \cdot L_{A} = \frac{11}{20} \times 2.2 = 1.21 m$

Solution

1 1.1

2 2.22

3 1.21

4 4.44

Ans.
(3)

$Given: \frac{Y_{A}}{Y_{B}} = \frac{20}{11}, A_{1} = A_{2}, F_{1} = F_{2}$

$Δ L_{1} = Δ L_{2} \Rightarrow \frac{F L_{A}}{A Y_{A}} = \frac{F L_{B}}{A Y_{B}}$

$L_{B} = \frac{Y_{B}}{Y_{A}} \cdot L_{A} = \frac{11}{20} \times 2.2 = 1.21 m$

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