Question

There are two wires of same material and same length. While the diameter of second wire is 2 times, the diameter of first wire. Then what will be the ratio of extension produced in the wire by applying same load ? 

(A) 1 : 1 

(B) 2 : 1 

(C) 1 : 2 

(D) 4 : 1

Answer 1

Correct option: (D) 4 : 1

Explanation:

ℓ = (FL / AY)

given: same force applied for same length of wire made up of some material. F, L & Y is constant

∴ ℓ ∝ (1/A)

ℓ ∝ (1 / r²)

given : r₂ = 2r₁ 

(ℓ₁ / ℓ₂) = (r₂ / r₁)² 

(ℓ₁ / ℓ₂) = 4     ∴  ℓ₁ : ℓ₂ = 4 : 1