In an experiment the values of two spring constants were measured as k₁ = (10 ± 0.2) N·m⁻¹ and k₂ = (20 ± 0.3) N·m⁻¹. If these springs are connected in parallel, then the percentage error in equivalent spring constant is :
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Question

In an experiment the values of two spring constants were measured as k₁ = (10 ± 0.2) N·m⁻¹ and k₂ = (20 ± 0.3) N·m⁻¹. If these springs are connected in parallel, then the percentage error in equivalent spring constant is :

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G1 Physics · Accepted Answer

For springs connected in parallel, K₍eq₎ = K₁+K₂. Therefore, K₍eq₎ = 10+20 = 30 N·m⁻¹. For addition, the maximum absolute errors add: ΔK₍eq₎ = ΔK₁+ΔK₂ = 0.2+0.3 = 0.5 N·m⁻¹. Hence the percentage error is % error = ΔK₍eq₎ ────── K₍eq₎ × 100 = 0.5 ───── 30 × 100 ≈ 1.67%. Correct option: D.