Parallel vs. Series Spring Configurations

Steps:

• In parallel, load L is shared, so each spring supports L/2 and extends x = (L/2)/k, giving k = L/(2x).
• In series, full load L acts on each spring, so each extends δ = L/k = L / (L/(2x)) = 2x.
• Total extension is sum of individual extensions: 2 × 2x = 4x.
• Effective spring constant in series is k/2, so total extension = L/(k/2) = 2L/k = 2 × (2x) = 4x.

Why D is correct:

• In series, springs add extensions under full load L, doubling the extension per spring compared to parallel (Hooke's law: F = kδ).

Why the others are wrong:

• A: ¼x confuses series with parallel stiffness (effective k doubles in parallel, not halves).
• B: x assumes same extension as parallel, ignoring increased force per spring in series.
• C: 2x assumes each spring still extends x, but full L doubles each extension to 2x.

Final answer: D