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Question #42256

Difficulty: 8/10 | 🟢 Free

The Question

Two concentric thin spherical shells of masses $M$ and $2M$ have radii $R$ and $2R$ respectively. What is the total gravitational potential energy stored in the gravitational field strictly in the region $r \geq 2R$ ?

Options

A.
$-\frac{9 G M^2}{4R}$
B.
$-\frac{5 G M^2}{4R}$
C.
$-\frac{5 G M^2}{2R}$
D.
$-\frac{9 G M^2}{2R}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Intuition_Breaker

Train your brain to resist "obvious" answers that are designed to deceive your intuition.

Concepts Behind This Question

Principle of Superposition|Gravitational Potential Energy (System)|Energy Density Partitioning

Why This Question Is Tricky

Common Mistakes

This question targets the misconception that gravitational potential energy obeys the principle of superposition linearly.

Students often incorrectly calculate the energy of the individual fields and add them ( $U_1 + U_2$ ), failing to realize that energy density depends on $g^2 = (g_1 + g_2)^2 \neq g_1^2 + g_2^2$ .

The cross-term represents the interaction energy.

By asking for the energy in a specific spatial region, it forces the use of energy density and exposes the non-linearity of energy partitioning.

Option B is the trap for linear superposition, and Option C is the trap for calculating the total energy of the entire system instead of the specified region.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Gravitation - Class 11 Part 1
Concept	Principle of Superposition
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free