Question

Two wires A and B of the same material and of equal length with the radii in the ratio 1 : 2 are subjected to identical loads. If the length of A increases by 8 mm, then the increase in length of B is:

विकल्प

• 2 mm

• 4 mm

• 8 mm

• 16 mm

Answer 1

2 mm

Explanation:

Ratio of radii, r₁ : r₂ = 1 : 2

Ratio of area, A₁ : A₂ = `π"r"_1^2:π"r"_2^2`

A₁ : A₂ = 1 : 4

Now, Stress₁ : Stress₂ = 4 : 1

So, Strain₁ : Strain₂ = 4 : 1

∴ `"l"_1/"l"_2 = 4/1`

⇒ 4l₂ = l₁ = 8

∴ l₂ = 2 mm

Increase in length of B is 2 mm.