On the surface of earth acceleration due to gravity is g and gravitational potential is V match

step 1 In this question, we have finding different values and the following table number two, which are

On the surface of earth acceleration due to gravity is g and...

On the surface of earth acceleration due to gravity is $\mathrm{g}$ and gravitational potential is $\mathrm{V}$ match the followingTable - 1 Table $-2$ (A) At height $\mathrm{h}=\mathrm{R}$ value of $\mathrm{g}$ (P) decrease by a factor $(1 / 4)$ (B) At depth $\mathrm{h}=(\mathrm{R} / 2)$ (Q) decrease by a factor $(1 / 2)$ (C) At height $\mathrm{h}=\mathrm{R}$ value of $\mathrm{v}$ (R) increase by a factor $(11 / 8)$ (D) At depth $\mathrm{h}=(\mathrm{R} / 2)$ value of $\mathrm{v}$ (S) increase by a factor 2 (T) None

On the surface of earth acceleration due to gravity is $\mathrm{g}$ and gravitational potential is $\mathrm{V}$ match the followingTable - 1 Table $-2$
(A) At height $\mathrm{h}=\mathrm{R}$ value of $\mathrm{g}$
(P) decrease by a factor $(1 / 4)$
(B) At depth $\mathrm{h}=(\mathrm{R} / 2)$
(Q) decrease by a factor $(1 / 2)$
(C) At height $\mathrm{h}=\mathrm{R}$ value of $\mathrm{v}$
(R) increase by a factor $(11 / 8)$
(D) At depth $\mathrm{h}=(\mathrm{R} / 2)$ value of $\mathrm{v}$
(S) increase by a factor 2
(T) None

Key Concepts

Shell Theorem

The shell theorem states that a spherically symmetric shell of mass exerts no net gravitational force on a particle located anywhere inside it, and that the gravitational force outside the shell is as if all the mass were concentrated at the center. This theorem is fundamental for understanding how only the mass enclosed within a certain radius contributes to the gravitational force at that radius, thus underpinning the calculations of gravitational acceleration and potential both inside and outside a spherical body like Earth.

Uniform Density Model of Earth

The assumption that the Earth has a uniform density simplifies the analysis of gravitational fields inside the Earth. In this model, the gravitational acceleration inside the Earth increases linearly from the center to the surface, and the gravitational potential follows a quadratic variation. This model is essential for estimating variations in both g and potential at different depths or heights when the true density distribution is approximated as constant.

Gravitational Acceleration Variation

Gravitational acceleration (g) is not constant at all distances from a massive body. Outside a spherically symmetric mass like the Earth, the acceleration decreases with the square of the distance; inside a uniformly distributed spherical mass, however, it typically varies linearly with the distance from the center. This understanding is crucial for calculating how g changes at different heights or depths relative to the Earth's surface.

Newton's Law of Universal Gravitation

This principle states that every pair of masses attracts each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. In the context of gravitational acceleration and potential near Earth, this law provides the fundamental relationship governing how gravitational effects diminish with increasing distance from the mass distribution.

Gravitational Potential

Gravitational potential is defined as the work done per unit mass to move an object from a reference point (often taken at infinity) to a specific point in a gravitational field. It reflects the energy landscape created by a mass distribution, and its variation with distance is different from that of gravitational acceleration, often involving an inverse relationship outside the mass and a quadratic variation inside under uniform density assumptions.

Please give Ace some feedback