13. You found a value for g of (10.00000 0.0001) m/s from your measurements. The

Question

13. You found a value for g of (10.00000 0.0001) m/s from your measurements. The theoretical value for g is 9.8 m/s2. a) Does your value agree with the theoretical? b) How confident are you in your agreement (or disagreement) with the theoretical value (how large is your random error)? c) Do you have significant sources of systematic error? 14. You found a value for g of (10.0+ 6.0) m/s? from your measurements. The theoretical value for g is 9.8 m/s2 39 68 a) Does your value agree with the theoretical? b) How confident are you in your agreement (or disagreement) with the theoretical value (how large is your random error)? c) Do you have significant sources of systematic error?

Explanation / Answer

13(a) Yes, the measured value agrees with the theoretical value, as it is more precise.

(b) As the measured acceleration due to gravity is 10.00000 m/ sec² and the error is 0.0001 m/sec². so we can say that absolute error in the result is 0.0001 and the relative error is 0.0001/10.00000= 0.00001 (0.001%). So we can say that the value for acceleration due to gravity is in error by 0.001% which gives more accurate result and acceptable value. In this case random error is almost negligible.

(c) in this case significant sources of systematic error is not possible.

14(a) No the measured value does not agrees with the theoretical value. As the value of error is too high and is beyond the acceptable range. It's not accurate and precise as well.

(b) As the measured acceleration due to gravity is 10.00000 m/sec² and the error is 6 m/sec² , so the relative error is 6/10 = 0.6 (60%) which is too high and can't give an acceptable value. In this case random errors may be present and perhaps it has a larger value.

(c) As errors may be present in the measuring instrument at the time of observation which is not corrected at that time which gives rises to source of systematic error.

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