Question

The length of rubber cord increase to 60 cm under a weight of 100 g suspended from it and to 70 cm under a weight of 120 g . Find the initial length of the cord . Also calculate the weight under which the length of the cord will become 74 cm .​

Answer 1

k = spring constant

L₀ = initial length of cord

L₁ = length of cord when 100 g weight is suspended = 60 cm

m = 100 g

using equilibrium of force

k (L₁ - L₀) = mg eq-1

L₂ = length of cord when 120 g weight is suspended = 70 cm

M = 120 g

using equilibrium of force

k (L₂ - L₀) = Mg eq-2

dividing eq-1 by eq-2

k (L₁ - L₀) /(k (L₂ - L₀)) = mg/(Mg)

(60 - L₀)/(70 - L₀) = 100/120

L₀ = 10 cm

using eq-1

k (L₁ - L₀) = mg

k (60 - 10) (0.01) = (0.1) (9.8)

k = 1.96 N/m

let the weight hanged be "m' "

L₂ = 74 cm

using equilibrium of force

k (L₂ - L₀) = m' g

(1.96) (0.74 - 0.1) = m' (9.8)

m' = 0.128 kg

m' = 0.128 x 1000 g

m' = 128 g

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