A group of 6 students make the following measurements of the speed of light (all

Question

A group of 6 students make the following measurements of the speed of light (all X 10 8 m/s): 3.03 +_0.04, 2.99+_0.03, 2.99+_0.02, 3.00+_0.05, 3.05+_0.04, 2.97+_0.02 what should the cohort report as their combined result? Is the reported value consistent with c(true)=299792459 m/s? If another student reports (3.0+_0.3) x 10 8 [m/s] Is there any change to the cohort's combined measurement? If a further student reports (4.01+_0.01) x 10 8 [m/s] Is there any change to the cohort's combined measurement?

Explanation / Answer

a. To find the combined result we have tu sum the magnitudes and it uncertainties:

3.03+2.99+2.99+3+3.05+2.97=18.03

0.04+0.03+0.02+0.05+0.04+0.02=0.2

Then, the combined result is: 18.03/6±0.2/6 = 3.005±0.033

b) The true value is included in the uncertaintie of the reported value, so they are consitent.

c) There will be a change in the combined mesaurement because is necessary to calculate a new average.

This new combined result will be: 3.004±0.0714       (with 7 measurements)

d) There will be a change in the combined mesaurement because is necessary to calculate a new average.

This new combined result will be: 3.13±0.06375       (with 7 measurements)

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