Two classmates want to examine the possible difference between inertial mass and gravitational mass using a simple-pendulum experiment. They suspend bobs of different compositions and masses from identical, lightweight strings of length 0.80m and measure the period of small-amplitude oscillations. Their data are summarized below.
Table 1 — Measured Periods of Identical-Length Pendulums
Bob material
Mass (kg)
Mean period T (s)
Brass
0.20
1.79
Wood
0.05
1.79
Steel
0.50
1.78
Assume all timing uncertainties are ±0.02s and length uncertainties are negligible.
(a) Derive an expression relating the measured period of a simple pendulum to the ratio of gravitational mass to inertial mass of the bob.
(b) Using the data in Table 1, determine whether the ratio of gravitational to inertial mass depends on the composition or amount of the bob. Show quantitatively how the data support your conclusion.
(c) Propose one modification to this experiment that would increase its sensitivity to a possible difference between the two types of mass. Justify how your modification would improve the measurement.