Question

The ratio of radii of two wires of same material is 2:1. If these wires are stretched by equal force, the ratio of stresses produced in them is

Answer 1

1:4 is the correct answer

Answer 2

Dear student,

Given :

• ratio of radii, r₁ : r₂ = 2 : 1
• wires are of same material meaning γ is same.
• forces acting are equal

To find :

• ratio of  stress produces in them

Solution :

∵   Stress = Force / Area

∴   Stress ∝ 1/ Area

From the above relation, we have :

 

      stress ∝ 1/ πr²

    stress₁/ stress₂ ∝ r₂²/ r₁²

    stress₁/ stress₂ ∝ 1 / 2²

    stress₁/ stress₂ ∝ 1/ 4

∴ The ratio of the stresses produces in them for stress₁/ stress₂ is 1 : 4.