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A block is suspended by a helical spring. The block is made to oscillate vertically with small amplitude If the error in measuring the time period of oscillation is 2% and that in measuring the mass is 1%, what is the maximum possible error in measuring the force constant of the spring?

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Detailed Solution

$T = 2 π \sqrt{\frac{m}{k}} \Rightarrow k = 4 π^{2} (\frac{m}{T^{2}}) ∴ (\frac{ΔK}{K} \times 100) % = (\frac{Δm}{m}) \times 100 % + 2 (\frac{ΔT}{T}) \times 100 % \begin{array}{l} = 1 % + 2 \times 2 % \\ = 5 % \end{array}$

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