Question

two wires made of material have lengths 3 m and 4 m and weight 18 gm amd 16 gm respectively. when they are subjected to the same tension, ratio of their elongation is​

Answer 1

Given,

Two wires made of material have lengths 3m and 4m and weight 18gm and 16gm respectively.

To find,

ratio of their elongation when they are subjected to the same tension.

from Young's modulus formula,

Y = FL/Al

where F is tension, A is cross sectional, L is length and l is elongation.

here, Y and F are constant. L/Al = constant

i.e., L₁/A₁l₁ = L₂/A₂l₂

⇒l₁/l₂ = (L₁/L₂) × (A₂/A₁) ......(1)

we know, mass = density × volume

⇒m = ρAL

so, m₁/m₂ = A₁L₁/A₂L₂

⇒18/16 = 9/8 = (A₁/A₂)(L₁/L₂)

⇒ (A₂/A₁) = 8/9 (L₁/L₂).........(2)

from equations (1) and (2) we get,

⇒l₁/l₂ = 8/9 × (L₁/L₂)² = 8/9 × (3/4)²

= 8/9 × 9/16 = 1/2

therefore ratio of elongation of wires is 1 : 2.