On a hypothetical exoplanet, careful experiments reveal that for every object the gravitational mass is 1.0 % larger than its inertial mass, while all other physical laws (including the value of the universal gravitational constant G) remain the same as on Earth. A researcher releases a rock of inertial mass mi from rest at height h above the planet’s surface, where the local gravitational field produced by the planet alone would have magnitude g0 if the two masses were exactly equal.
(a) Derive an expression for the rock’s free-fall acceleration afall in terms of g0 and the 1.0 % mass discrepancy described above.
(b) When the rock has fallen halfway to the ground (distance h/2), determine the ratio of its gravitational potential energy change to the kinetic energy gained, expressed in terms of the 1.0 % discrepancy.
(c) Describe two observable consequences or paradoxes that inhabitants of this planet might notice in everyday life if inertial and gravitational mass differed by 1.0 %.