If the value of ' g ' acceleration due to gravity, at earth...

If the value of ' $\mathrm{g}$ ' acceleration due to gravity, at earth surface is $10 \mathrm{~ms}^{-2}$. its value in $\mathrm{ms}^{-2}$ at the center of earth, which is assumed to be a sphere of Radius ' $\mathrm{R}$ 'meter and uniform density is (A) 5 (B) $10 / \mathrm{R}$ (C) $10 / 2 \mathrm{R}$ (D) zero

If the value of ' $\mathrm{g}$ ' acceleration due to gravity, at earth surface is $10 \mathrm{~ms}^{-2}$. its value in $\mathrm{ms}^{-2}$ at the center of earth, which is assumed to be a sphere of Radius ' $\mathrm{R}$ 'meter and uniform density is
(A) 5
(B) $10 / \mathrm{R}$
(C) $10 / 2 \mathrm{R}$
(D) zero

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Key Concepts

Newton's Shell Theorem

Newton's shell theorem states that a spherically symmetric body affects external objects gravitationally as if all its mass were concentrated at its center, and that within a spherical shell, the net gravitational force is zero. This concept is fundamental when analyzing the gravitational field at various points inside a spherical body, such as the Earth.

Uniform Density Sphere

Assuming a sphere has uniform density simplifies calculations of the gravitational field inside the sphere. With uniform density, the gravitational force inside the sphere is directly proportional to the distance from the center, which means it linearly decreases to zero as one approaches the center.

Gravitational Field in a Uniform Sphere

In a sphere with uniform density, only the mass enclosed within a given radius contributes to the gravitational force at that point. Therefore, at the center of the sphere, the enclosed mass is zero, leading to zero gravitational acceleration. Understanding this variation of the gravitational field inside a spherical body is crucial for analyzing problems related to gravity within planets.

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