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Question #42350

Difficulty: 8/10 | 🟢 Free

The Question

A uniform solid sphere of mass $M$ and radius $R$ is restructured into a thin spherical shell of the same mass $M$ and radius $R$ . The minimum energy required for this restructuring is $E_0$ . A particle of mass $m$ is initially in a circular orbit of radius $2R$ around the solid sphere. The particle is given an instantaneous additional kinetic energy equal to $E_0$ , and its velocity vector is simultaneously redirected to point radially inwards towards the center. It enters the newly formed shell through a small hole. Inside the shell, the particle experiences a constant non-conservative drag force of magnitude $f$ . If the particle comes to rest exactly at the center of the shell, what is the value of $f$ ?

Options

A.
$\frac{GM}{R^2} \left( \frac{M}{10} + \frac{5m}{4} \right)$
B.
$\frac{GM}{R^2} \left( \frac{M}{10} + \frac{m}{2} \right)$
C.
$\frac{GM}{R^2} \left( \frac{11M}{10} + \frac{3m}{4} \right)$
D.
$\frac{GM}{R^2} \left( \frac{M}{10} + \frac{3m}{4} \right)$

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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

Conservative vs Non-conservative|Shell Theorem (Internal vs External)|Gravitational Self-Energy|Orbital Velocity Energy Balance

Why This Question Is Tricky

Common Mistakes

This question tests the synthesis of gravitational self-energy, orbital mechanics, and the Shell Theorem.

The primary trap is the misapplication of energy conservation inside the shell.

Students often incorrectly assume the gravitational potential continues to decrease towards the center (as it would in a solid sphere), leading them to add spurious gravitational work to the kinetic energy (Option A).

It also rigorously tests the precise calculation of self-energy difference and the inclusion of initial orbital kinetic energy before applying the Work-Energy Theorem in a non-conservative regime.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Work, Energy, and Power - Class 11 Part 1
Concept	Conservative vs Non-conservative
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free