Acceleration due to gravity at depth
Variation of g with Depth :
When we discuss how the acceleration due to gravity (g) changes with depth inside the Earth, we must take into account the distribution of mass within the Earth. According to the shell theorem, the gravitational force inside a spherical shell of uniform density behaves in a way that only the mass enclosed within a spherical shell at a radius smaller than the point where the object is located contributes to the gravitational force.
Concept of Earth's Structure: The Earth can be imagined as a sphere made up of many concentric uniform spherical shells. Each shell has a certain mass, and the total mass of the Earth is the sum of the masses of all these shells. When an object is at the Earth's surface, it experiences the gravitational pull as if the total mass of the Earth is concentrated at the center of the Earth (this is because of the spherical symmetry). However, as we go deeper into the Earth, the situation changes.
Consider a body of mass m on the surface of the Earth. The acceleration due to gravity on the Earth’s surface is given by,
Consider a body at a point P at the depth d below the surface of the Earth . The net force on P is only due to the material inside the inner sphere of radius OP = R - d. Acceleration due to gravity because of this sphere is
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