Consider two springs with elasticity coefficients k1, k2 in the two cases: (a) a spring connected in series and stretched by a load P and (b) two springs hanging in parallel and stretched by the same load

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Question

Consider two springs with elasticity coefficients k₁, k₂ in the two cases: (a) a spring connected in series and stretched by a load P and (b) two springs hanging in parallel and stretched by the same load

The distance descended by load to reach equilibrium can't be same in both cases.

If k₁ = k₂ sum total of extension in both spring in case-A exceeds sum total of extension in both springs in case-B.

If k₁ = k₂, sum total of extension in both springs in case-A equals the sum total of extension in both spring in case-B.

Elastic potential energy in both cases can't be same.

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k_eq same
⇒ $\frac{k_{1} k_{2}}{k_{1} + k_{2}}$ = k₁ + k₂
⇒ k₁k₂ = (k₁ + k₂)² Not possible

$\frac{1}{2}$ kx² = $\frac{1}{2}$ mgx = $\frac{1}{2}$ mg mg/kg = $\frac{m^{2} g^{2}}{2 k_{eq}}$

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