Physics

Physics

Problem

Four points are defined relative to Earth’s surface (radius 6400 km6400\,\text{km}): A: on the surface B: at an altitude of 480 km480\,\text{km} C: at a depth of 480 km480\,\text{km} D: at an altitude of 960 km960\,\text{km} Which option gives the correct order of the magnitudes of acceleration due to gravity at these points, from greatest to least? a) C>A>B>DC > A > B > D b) A>C>B>DA > C > B > D c) A>B>C>DA > B > C > D d) C>B>A>DC > B > A > D
Intuitive explanation

Gravitational acceleration depends on both distance from Earth's center and the mass distribution below you. Points closer to the center experience stronger gravity, but once you go underground, only the mass in the sphere below you counts—the shell above contributes nothing. This means point C (deep underground) has less mass pulling on it than surface point A, even though it's closer to the center. Compare distances and effective masses carefully to rank them.

Intuitive explanation

Gravitational acceleration depends on both distance from Earth's center and the mass distribution below you. Points closer to the center experience stronger gravity, but once you go underground, only the mass in the sphere below you counts—the shell above contributes nothing. This means point C (deep underground) has less mass pulling on it than surface point A, even though it's closer to the center. Compare distances and effective masses carefully to rank them.

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