A particle of mass M is situated at the center of a...

A particle of mass $\mathrm{M}$ is situated at the center of a spherical shell of same mass and radius a the magnitude of gravitational potential at a point situated at (a/2) distance from the center will be (A) $[(4 \mathrm{GM}) / \mathrm{a}]$ (B) $(\mathrm{GM} / \mathrm{a})$ (C) $[(2 \mathrm{GM}) / \mathrm{a}]$ (D) $[(3 \mathrm{GM}) / \mathrm{a}]$

A particle of mass $\mathrm{M}$ is situated at the center of a spherical shell of same mass and radius a the magnitude of gravitational potential at a point situated at (a/2) distance from the center will be
(A) $[(4 \mathrm{GM}) / \mathrm{a}]$
(B) $(\mathrm{GM} / \mathrm{a})$
(C) $[(2 \mathrm{GM}) / \mathrm{a}]$
(D) $[(3 \mathrm{GM}) / \mathrm{a}]$

Key Concepts

Superposition Principle

The superposition principle in gravitation states that the total gravitational potential at a point is the algebraic sum of the potentials due to each individual mass configuration. This principle is used to combine contributions from a central point mass and a surrounding spherical shell to find the overall gravitational potential at any given point.

Spherical Shell Theorem

The spherical shell theorem states that a spherically symmetric mass distribution affects external objects as if all the mass were concentrated at its center, and that inside a thin spherical shell the gravitational force is zero while the potential remains constant. This concept is crucial when calculating the gravitational potential at a point inside or on the surface of a spherical shell.

Gravitational Potential

Gravitational potential is defined as the work done per unit mass in bringing a test mass from infinity to a point in a gravitational field. It is a scalar quantity and is given by the formula ? = -GM/r for a point mass, which allows easy calculation by summing contributions from different masses when using the superposition principle.

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