In a lab, a spring–mass system is constructed using a mass. The period of small…

PHYSICS · Single correct · A Level · Physics · Measurements and their errors · Measurements and their errors

Problem

In a lab, a spring–mass system is constructed using a 0.300 kg (±0.005 kg)0.300\,\text{kg}\,(\pm 0.005\,\text{kg}) mass. The period of small oscillations is measured as 1.10 s (±0.02 s)1.10\,\text{s}\,(\pm 0.02\,\text{s}). Which of the following is the best statement of the spring constant with its combined percent uncertainty (use simple percent-addition for small uncertainties)? (a) 12.3 N ⁣⋅ ⁣m−1  ±2%12.3\,\text{N}\!\cdot\!\text{m}^{-1}\;\pm 2\% (b) 9.8 N ⁣⋅ ⁣m−1  ±2%9.8\,\text{N}\!\cdot\!\text{m}^{-1}\;\pm 2\% (c) 9.8 N ⁣⋅ ⁣m−1  ±5%9.8\,\text{N}\!\cdot\!\text{m}^{-1}\;\pm 5\% (d) 7.0 N ⁣⋅ ⁣m−1  ±5%7.0\,\text{N}\!\cdot\!\text{m}^{-1}\;\pm 5\%

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