Question

The ratio of diameter of two wires of same material is n : 1 the length of wires are 4 m each. On applying the same load. What will be the increase in length of their wires? 

(A) n² times 

(B) n times 

(C) 2n times 

(D) None of the above

Answer 1

Correct option: (A) n² times

Explanation:

Y = (FL / Aℓ)  i.e.      ℓ = (FL / AY)

Material is same hence Y is same. Applied force is same.

Length of both wires same

i.e.      Y, F, L is constant

hence ℓ ∝ 1/A

i.e. ℓ ∝ (1 / r²)

∴ (ℓ₁ / ℓ₂) = (r₂ / r₁)² 

given : (r₁ / r₂) = (n/1)

hence (ℓ₁ / ℓ₂) = (1 / n²)

i.e. ℓ₂ = n² ∙ ℓ₁