Question

Two wires are made of the same material and have the same volume. However, wire 1 has cross-sectional area A and wire 2 has cross-sectional Area 3A. If the length of wire 1 increases by on applying force F. How much force is needed to stretch wire 2 by same amount. 

(A) F 

(B) 4F 

(C) 6F 

(D) 9F

Answer 1

Correct option: (D) 9F

Explanation:

Young's modulus = Y = (F/A) / (ℓ/L) = (F/L) / (A/ℓ)             (1)

Also V = A × L (volume = area × length)

∴ (V/A) = L

From (1) Y = (FV / A²ℓ)      i.e. F = [(YA²ℓ) / V]

i.e.  F ∝ A² 

(F₁ / F₂) = (A₁ / A₂)² 

Given : A₁ = A and A₂ = 3A hence

(F₁ / F₂) = (1/9) hence F₂ = 9F₁ 

i.e. F₂ = 9F ------- given F₁ = F