Question

Why how much a rubber string of length 10 cm increase in length under its own weight when suspended?

Answer 1

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Answer 2

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here is ur answer...

    [Density of rubber is 1500 (kg / m3), Y = 5 × 108 (N / m2),

                                        g = 10 (m / s2)]

                                        (A) 15 × 10–4m                 (B) 7.5 × 10–4 m

                                        (C) 12 × 10–4m                 (D) 25 × 10–4 m

 

Solution:                 Answer         (A) 15 × 10–4 m

                    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   

hope it helps...

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