Question

The dimensions of four wires of the same material are given below, in which wire the increase in length will be maximum when the same strain is applied. 

(A) Length 100 cm, Diameter 1 mm 

(B) Length 200 cm, Diameter 2 mm 

(C) Length 300 cm, Diameter 3 mm 

(D) Length 50 cm, Diameter 0.5 mm

Answer 1

Correct option: (D) Length 50 cm, Diameter 0.5 mm

Explanation:

Y = [(F/A) / (ℓ/L)] = [(FL) / (ℓA)]     i.e.      ℓ = (FL / YA)

hence ℓ ∝ L/A --------- as F is same

Area = A = π(d/2)² 

Hence

ℓ ∝ (L / d²)

(A) (L / d²) = [(100) / (0.1)²] = 10000

(B) (L / d²) = [(200) / (0.2)²] = 5000

(C) (L / d²) = [(300) / (0.3)²] = 3333

(D) (L / d²) = [(50) / (0.05)²] = 20000

Hence ℓ is maximum for D option.