A uniform metallic wire is elongated by 0 . 04 m when subjected to a linear force F . The elongation, if its length and diameter is doubled and subjected to the same force will be _________ cm .

Step-by-step solution

F = Y . A · Δ l l ⇒ Δ l = F Y . A . · l ⇒ Δ l = F . l Y . π r 2 ⇒ Δ l ∝ l r 2 Δ l 2 Δ l 1 = l 2 l 1 r 1 r 2 2 = 2 1 2 2 ⇒ Δ l 2 Δ l 1 = 1 2 ⇒ Δ l 2 = Δ l 1 2 = 0 . 04 2 = 0 . 02   m ⇒ Δ l 2 = 2   cm .