Under the same load, wire A having length 5.0 m and cross section 2.5 10^-5 m^2 stretches uniformly by the same amount a

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Under the same load, wire A having length 5.0 m and cross section 2.5 10^-5 m^2 stretches uniformly by the same amount as another wire B of length 6.0 m and a cross section of 3.0 10^-5 m^2. The…

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Given: Same load acts on both wires and both wires have the same elongation. For wire A, $L_A = 5.0 \, \text{m}$ and $A_A = 2.5 \times 10^{-5} \, \text{m}^2$ . For wire B, $L_B = 6.0 \, \text{m}$ and $A_B = 3.0 \times 10^{-5} \, \text{m}^2$ .

Find: The ratio $\dfrac{Y_A}{Y_B}$ .

Young's modulus is given by

Y = \frac{F L}{A \, \Delta L}

where $F$ is the load, $L$ is the length, $A$ is the cross-sectional area, and $\Delta L$ is the elongation.

Since the load and elongation are the same for both wires,

\frac{Y_A}{Y_B} = \frac{L_A A_B}{L_B A_A}

Substituting the given values,

\frac{Y_A}{Y_B} = \frac{5 \times 3.0 \times 10^{-5}}{6.0 \times 2.5 \times 10^{-5}} = 1

Therefore, the ratio of the Young's modulus of wire A to wire B is $1:1$ . The correct option is B.

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