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Two wires of the same length and radius are joined end to end and loaded. The Young's moduli of the materials of the two wires are Y₁ and Y₂. The combination behaves as a single wire; then its Young's modulus is

Asked in JEE Main 25th July 1st Shift 2021 · Series and parallel wires

• (1) (2Y₁Y₂)/(Y₁+Y₂)
• (2) (Y₁Y₂)/(Y₁+Y₂)
• (3) (Y₁Y₂)/(2(Y₁+Y₂))
• (4) (2Y₁Y₂)/(3(Y₁+Y₂))

Step-by-step solution

Why the other options are wrong

• (2) comes from copying the resistors-in-parallel formula straight across and forgetting that the equivalent wire has length 2L, not L; that missing factor of 2 is exactly what turns this into the correct expression.
• (3) comes from making the same length slip and then dividing by 2 as well, as if the two moduli had to be averaged on top of being combined.
• (4) comes from writing the total length as 3L instead of 2L, usually by counting the equivalent wire as a third piece alongside the two originals.

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