Suppose the smallest division on the scale of the timing device is t, the reaction time of a normal person os t', which one should be used for estimating the incertainty on the measurement of period T after a single timing activity? Explain briefly.

The reaction time delay, if always the same, will not affect the measurement of an intervsal of time, since it affects both the beginning and the end of the interval T in the same way. However, reaction time can vary from one measurement to another. I would estimate the rms variation in reaction time to be about t'/3, resulting in an interval measurement error of 0.47 t' and a total measurement error (standard deviation) of about sqrt(t^2 + 0.2 t'^2)

This is probably not the answer they are expecting. They probably want you to say t.

When estimating the uncertainty on the measurement of period T after a single timing activity, we should consider the smallest division on the scale of the timing device (t) rather than the reaction time of a normal person (t').

The reason for this is that the smallest division on the scale of the timing device (t) represents the smallest increment of time that can be measured by the device. This means that any timing activity performed with the device can only have a precision up to t. So, while the reaction time of a normal person (t') may introduce some additional uncertainty, it is generally much larger than the smallest division on the scale of the timing device.

In other words, the reaction time of a person (t') is a personal factor that varies from individual to individual and can significantly vary in different scenarios. On the other hand, the smallest division on the scale of the timing device (t) is a fixed limitation of the measuring instrument itself and represents its inherent precision.

Therefore, when estimating uncertainty in a measurement, we should focus on the instrument's precision represented by the smallest division on the scale (t). This is because it provides a more accurate representation of the device's capability to measure time intervals, regardless of the reaction time of the person operating it.