In an experiment to determine the acceleration of free fall the period of oscillation of and length of a simple pendulum were measured. The uncertainty in the measurement of was estimated to be 4% and that of , 1%. The value of was determined using the formula =4pi^2l | t^2 what is the percentage uncertainty in the calculated value of g?
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Answer:
Time period, T=2π
g
l
or g=
T
2
4π
2
l
The maximum percentage error
g
Δg
=
l
Δl
+2
∣
∣
∣
∣
∣
T
ΔT
∣
∣
∣
∣
∣
where
l
Δl
=2% and
T
ΔT
=3%
g
Δg
=2%+2×3%
=2%+6%=8%
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