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Question #42280

Difficulty: 8/10 | 🟢 Free

The Question

A uniform solid sphere of mass $M$ and radius $R$ carries a total charge $Q$ uniformly distributed throughout its volume. The gravitational potential $V_g$ produced by the sphere is defined to be zero at infinity. The electrostatic potential $V_e$ produced by the sphere is defined to be zero at its surface. A point particle of mass $m$ and charge $q$ is placed at the center of the sphere. What is the potential energy of the point particle in the fields of the sphere?

Options

A.
$\frac{qQ}{8\pi\epsilon_0 R} - \frac{3GMm}{2R}$
B.
$\frac{3qQ}{8\pi\epsilon_0 R} - \frac{3GMm}{2R}$
C.
$\frac{qQ}{8\pi\epsilon_0 R} - \frac{GMm}{2R}$
D.
$\frac{qQ}{4\pi\epsilon_0 R} - \frac{GMm}{R}$

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Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Multi-Concept_Bridge

Master problems that require linking physics and math concepts to solve complex competitive questions.

Concepts Behind This Question

Gravitational Potential Energy (System)|Superposition of Potentials|Reference Potential Convention

Why This Question Is Tricky

Common Mistakes

This question tests the student's understanding of reference points in potential fields and the distinction between potential difference and absolute potential energy.

Students often memorize the standard formulas for the potential at the center of a solid sphere (which is 3/2 times the surface potential) assuming the reference is at infinity.

The trap forces them to apply a reference shift to the electrostatic potential while keeping the standard reference for the gravitational potential.

A common mistake is to either ignore the electrostatic reference shift entirely (yielding Option B) or to incorrectly apply the surface reference to the gravitational potential as well (yielding Option C).

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Gravitation - Class 11 Part 1
Concept	Gravitational Potential Energy (System)
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free