Assuming earth to be a sphere of a uniform density, what is...

Assuming earth to be a sphere of a uniform density, what is value of gravitational acceleration in mine $100 \mathrm{~km}$ below the earth surface $=\ldots \ldots \ldots \ldots \mathrm{ms}^{-2}$
(A) $9.66$
(B) $7.64$
(C) $5.00$
(D) $3.1$

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Key Concepts

Shell Theorem

The Shell Theorem is a principle in classical gravitation which states that a spherically symmetric shell of mass exerts no net gravitational force on an object located inside it. This theorem is crucial when calculating gravitational effects within a sphere, as it allows the problem to be reduced to considering only the mass enclosed within a given radius.

Gravitational Acceleration Inside a Uniform Sphere

When determining the gravitational acceleration inside a sphere with uniform density, the acceleration is directly proportional to the distance from the center. This linear relationship arises because only the mass inside the radius of interest contributes to the gravitational force, leading to an expression that is a fraction of the surface gravitational acceleration.

Uniform Density

This concept refers to the assumption that a spherical body, like the Earth in this problem, has the same density at all points throughout its volume. This simplification makes it possible to derive mathematical expressions for gravitational effects, since the mass distribution is constant and symmetrical.

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