To find the spring constant (k) of a spring experimentally, a student commits 2% positive error in the measurement of time and 1% negative error in measurement of mass. The percentage error in determining value of k is :
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Question

To find the spring constant (k) of a spring experimentally, a student commits 2% positive error in the measurement of time and 1% negative error in measurement of mass. The percentage error in determining value of k is :

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G1 Physics · Accepted Answer

For a mass-spring system: T = 2π√(m/k) Therefore: k = 4π²m/T² For signed percentage errors: Δk/k = Δm/m - 2ΔT/T Given: Δm/m = -1% ΔT/T = +2% So: Δk/k = -1% - 2(2%) = -5% Hence the magnitude of percentage error is: 5%