A mild steel wire of length 2 L and cross-sectional area A is stretched, well with in the elastic limit, horizontally between two pillars as shown in figure. A mass m is suspended from the mid-point of the wire strain in the wire is

Question

A mild steel wire of length 2 L and cross-sectional area A is stretched, well with in the elastic limit, horizontally between two pillars as shown in figure. A mass m is suspended from the mid-point of the wire strain in the wire is, x 2 2 L 2, x L, x 2 L, x 2 2 L

MARKS App · Accepted Answer

Increase in length Δ L = B O + O C - B C = 2 B O - 2 B D ⇒ Δ L = 2 B O - 2 L = 2 L 2 + x 2 1 2 - 2 L or Δ L = 2 L 1 + x 2 L 2 1 2 - 2 L [ ∵ using Bionomial theorem] ⇒ Δ L ≈ 2 L 1 + 1 2 x 2 L 2 - 1 = x 2 L ∵ x L ∴ Strain = Δ L 2 L = 1 2 L × ∆ L = 1 2 L × x 2 L = x 2 2 L 2 .

Search any question & find its solution

Looking for more such questions to practice?