Two identical sealed research modules, Module A and Module B, are delivered to different locations:
• Module A is placed at rest on a planet’s surface where the local gravitational field strength is unknown.
• Module B is mounted inside a spacecraft that is far from all massive bodies but accelerates "upward" with constant magnitude a.
An investigator inside each module performs the following experiment: a simple pendulum of length L=1.00m is set into small-angle oscillation, and the period is measured to be T=2.01s in each module.
(a) Assuming the period measurement is accurate, determine the numerical value of a for Module B.
(b) Using the same data, determine the gravitational field strength gplanet at the surface where Module A rests.
(c) Considering only measurements possible entirely within a single sealed module, explain whether the investigator can distinguish Module A from Module B. Support your answer with specific reference to experimental outcomes.
(d) Suppose that while the pendulum is oscillating in Module B, the spacecraft’s engines suddenly shut off so that the module enters inertial motion with negligible residual acceleration. Qualitatively describe what will happen to the pendulum’s motion immediately after engine shut-down, and explain how this observation could reveal the change to the investigator.