Two wires of same length and radius are joined end to end and loaded. The Young's moduli of the materials of the two wires are Y 1 and Y 2 . The combination behaves as a single wire then its Young's modulus is:

Step-by-step solution

In series combination, Δ l = ℓ 1 + ℓ 2 Y = F / A Δ ℓ / ℓ ⇒ Δ ℓ = F ℓ A Y ⇒ Δ ℓ ∝ ℓ Y Equivalent length of rod after joining is = 2 ℓ As, lengths are same and force is also same in series Δ ℓ = Δ ℓ 1 + Δ ℓ 2 ℓ eq Y eq = ℓ Y 1 + ℓ Y 2 ⇒ 2 ℓ Y = ℓ Y 1 + ℓ Y 2 ∴   Y = 2 Y 1 Y 2 Y 1 + Y 2