Physics
Physics
Problem
A mass weighs on Earth’s surface. The mass is first lowered into a mine to a depth of and later lifted to a certain altitude above the surface such that its weight becomes exactly the same as inside the mine. Take Earth’s radius . Answer the following. a. (i) Calculate the weight of the mass at the depth. b. (ii) Determine the altitude above the surface at which the mass will have the same weight as inside the mine. c. (iii) State whether the mass of the body has changed in either process and justify your answer briefly.Intuitive explanation
The key insight is that weight depends on gravitational field strength, which changes predictably with distance from Earth's center—both when you go down into a mine and when you go up into the atmosphere. You'll need to find how varies at depth (accounting for the shell theorem: only the mass below you counts) and at altitude (where you're simply farther from Earth's center), then set those two weights equal to find the mystery altitude.
Intuitive explanation
The key insight is that weight depends on gravitational field strength, which changes predictably with distance from Earth's center—both when you go down into a mine and when you go up into the atmosphere. You'll need to find how varies at depth (accounting for the shell theorem: only the mass below you counts) and at altitude (where you're simply farther from Earth's center), then set those two weights equal to find the mystery altitude.