Question

Two wires A & B are of same materials. Their lengths in the ratio 1 : 2 and diameters are in the ratio 2 : 1 when stretched by force F_A and F_B respectively, they get equal increase in lengths Then the ratio (F_A / F_B) should be.......... 

(A) 1 : 2 

(B) 1 : 1 

(C) 2 : 1 

(D) 8 : 1

Answer 1

Correct option: (D) 8 : 1

Explanation:

Material is same hence Y is same.

Increment in length ℓ is same.

(L₁ / L₂) = (1/2)

(R₁ / R₂) = (2/1)

∵ Y = (FL / Aℓ)   i.e. F = (YAℓ / L)

here Y, ℓ is constant

∴ F ∝ A/L

∴ (F₁ / F₂) = (A₁ / A₂) ∙ (L₂ / L₁) ∙ (R₁ / R₂)² 

∴ (F₁ / F₂) = 2 × (2)² = 8

i.e. (F_A / F_B) = (8/1)