A uniform steel wire hangs from the ceiling and elongates due to its own weight. The ratio of elongation of the upper half of the wire to the elongation of the lower half of wire is

Question

TestHub · Accepted Answer

Let the wire have length L , weight W , area A . Tension at distance y from the top: L W ( L − y ) ​ Upper half: Δ u ​ = A Y L W ​ ∫ 0 L /2 ​ ( L − y ) d y = A Y L W ​ ⋅ 8 3 L 2 ​ Lower half: Δ l ​ = A Y L W ​ ∫ L /2 L ​ ( L − y ) d y = A Y L W ​ ⋅ 8 L 2 ​ Δ l ​ Δ u ​ ​ = 1 3 ​

Physics - Elasticity Question with Solution | TestHub

Options:

Doubts & Discussion