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Q.

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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a

0.2%

b

0.1%

c

0.5%

d

5%

answer is A.

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Detailed Solution

T=tn and ΔT=Δtn ΔTT×100=Δtt×100=0.12×100×100=0.05%  %Δll×100=0.1 cm100 cm×100=0.1% T=2πlg ⇒g=4π2lT2∝IT2 % error in g=(% error in l)+2(% error in T) =0.1%+2(0.05%)=0.2%
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