Question

A rubber cord 10 m long is suspended vertically. How much does it stretch under its own weight. [Density of rubber is 1500 (kg / m³), Y = 5 × 10⁸ (N / m²), g = 10 (m / s²)] 

(A) 15 × 10^–4 m 

(B) 7.5 × 10^–4 m 

(C) 12 × 10^–4 m 

(D) 25 × 10^–4 m

Answer 1

Correct option: (A) 15 × 10^–4 m

Explanation:

W = weight of the cord = mg

as density = [{mass} / {volume}]   i.e. d = m/v

∴ W = g ∙ d ∙ v

W = g ∙ d ∙ A ∙ L -------- volume = area × length

∴ W = 10 × 1500 × A × 10

W = 15A × 10⁴ N

Stress = W/A

= {(15A × 10⁴) / A}

Stress = 15 × 10⁴ N/m² 

As the weight of rubber acts at centre of gravity only upper half of length is stretched.

i.e.      L' = (10 / 2) = 5 cm

∴ strain = (ℓ / L') = (ℓ/5) = [(stress) / Y]

∴ (ℓ/5) = [{15 × 10⁴} / {5 × 10⁸}] = 15 × 10^–4 m