Question

A wire elongates by 1 mm when a load W is hanged from it. If the wire goes ever a pulley and two weight W each are hang at the two ends. What will be the elongation of the wire? (in mm) 

(A) 2ℓ 

(B) zero 

(C) ℓ/2 

(D) ℓ

Answer 1

Correct option: (D) ℓ

Explanation:

∵ Y = (FL / Aℓ)

i.e. ℓ = (WL / AY)            (1)

When wire is passed over the pulley, let ℓ¹ be increase in the length of each segment (length of each segment = L/2)

 ∴ Y = [{W(L/2)} / {Aℓ¹}]

ℓ¹ = [{WL} / {AY2}] = [(WL) / (AY)] × (1/2)

from (1)

ℓ¹ = (ℓ/2)

∴ Total increase in length = ℓ¹ + ℓ¹ = 2ℓ¹ = (2ℓ / 2) = ℓ