The length of a simple pendulum is about $$100$$ cm known to have an accuracy of $$1$$ mm. Its period of oscillation is $$2$$ s determined by measuring the time for $$100$$ oscillations using a clock of $$0.1$$ s resolution. What is the accuracy in the determined value of g?

Question

The length of a simple pendulum is about $$100$$ cm known to have an accuracy of $$1$$ mm. Its period of oscillation is $$2$$ s determined by measuring the time for $$100$$ oscillations using a clock of $$0.1$$ s resolution. What is the accuracy in the determined value of g?

Infinity Learn · Accepted Answer

$$T=tn$$ and Δ$$T=$$Δtn ΔTT×$$100=$$Δtt×$$100=0.12$$×$$100$$×$$100=0.05$$%  %Δll×$$100=0.1$$ $$cm100$$ cm×$$100=0.1$$% $$T=2$$$$π$$lg ⇒$$g=4$$$$π$$$$2lT2$$∝$$IT2$$ % error in $$g=($$% error in $$l)+2($$% error in $$T)$$ $$=0.1$$%$$+2(0.05$$%$$)=0.2$$%

The length of a simple pendulum is about $100 cm$ known to have an accuracy of $1 mm$ . Its period of oscillation is $2 s$ determined by measuring the time for 100 oscillations using a clock of $0.1 s$ resolution. What is the accuracy in the determined value of g?

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The length of a simple pendulum is about 100 cm known to have an accuracy of 1 mm. Its period of oscillation is 2 s determined by measuring the time for 100 oscillations using a clock of 0.1 s resolution. What is the accuracy in the determined value of g?

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Ready to Test Your Skills?

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The length of a simple pendulum is about $100 cm$ known to have an accuracy of $1 mm$ . Its period of oscillation is $2 s$ determined by measuring the time for 100 oscillations using a clock of $0.1 s$ resolution. What is the accuracy in the determined value of g?