Assuming the earth to have a constant density, point out...

Assuming the earth to have a constant density, point out which of following curves show the variation acceleration due to gravity from center of earth to points far away from the surface of earth $\ldots \ldots \ldots \ldots$

Key Concepts

Newton's Law of Gravitation

This law states that the gravitational force between two masses is proportional to the product of their masses and inversely proportional to the square of the distance between them. It is the foundational principle for understanding how gravitational acceleration behaves both near and far from a mass like the Earth.

Gravitational Field Inside a Uniform Sphere

Inside a sphere with constant density, only the mass enclosed within a given radius contributes to the gravitational force at that point. As a result, gravitational acceleration increases linearly with distance from the center, reaching a maximum at the surface.

Gravitational Field Outside a Uniform Sphere

Outside a uniform sphere, the entire mass of the sphere can be considered as concentrated at its center. Therefore, the gravitational acceleration follows an inverse square law, decreasing as the square of the distance from the center.

Constant Density Assumption

Assuming constant density simplifies the calculation of gravitational effects inside a spherical body. It allows the enclosed mass to be directly related to the volume (and thus to the cube of the radius), leading to a linear variation of gravitational acceleration inside the sphere and a standard inverse square decay outside.

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