A spring is suspended from a fixed point and a force is applied. The position of a pointer attachedto the bottom of the spring against a vertical ruler is recorded.Before the force is applied, the position of the pointer is (225 2) mm.After the force is applied, the position of the pointer is (250 2) mm.The extension of the spring is determined.What is the percentage uncertainty in the extension?A 1.6% B 1.8% C 8.0% D 16%
Question
A spring is suspended from a fixed point and a force is applied. The position of a pointer attachedto the bottom of the spring against a vertical ruler is recorded.Before the force is applied, the position of the pointer is (225 2) mm.After the force is applied, the position of the pointer is (250 2) mm.The extension of the spring is determined.What is the percentage uncertainty in the extension?A 1.6% B 1.8% C 8.0% D 16%
Solution
The extension of the spring is the difference in the position of the pointer before and after the force is applied.
So, the extension = (250 ± 2) mm - (225 ± 2) mm = (25 ± 4) mm
The uncertainty in the extension is the sum of the uncertainties before and after the force is applied, which is 2 mm + 2 mm = 4 mm.
The percentage uncertainty in the extension is calculated by dividing the absolute uncertainty by the measured value and then multiplying by 100%.
So, the percentage uncertainty = (4 mm / 25 mm) * 100% = 16%
Therefore, the answer is D 16%.
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