A wire has lengths l₁ and l₂ under tensions 100 N and 120 N respectively. If 10l₂ = 11l₁ and the natural length is l₁/x, find x.

Question

G1 Physics · Accepted Answer

For elastic extension, F = k(l - l₀). 100 = k(l₁ - l₀) 120 = k(l₂ - l₀), with l₂ = 1.1l₁. Dividing: 1.2 = (1.1l₁ - l₀)/(l₁ - l₀). 1.2l₁ - 1.2l₀ = 1.1l₁ - l₀ 0.1l₁ = 0.2l₀ l₀ = l₁/2. Thus x = 2.