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Question #42094
The Question
A geostationary satellite consists of a main body of mass and a payload of mass connected by a massless rigid arm of length . The center of mass of the system is in a stable circular orbit of radius around the Earth with an orbital angular velocity . An internal motor causes the arm to rotate in the orbital plane such that the payload revolves around the main body with a constant angular speed relative to the inertial frame. Which of the following represents the maximum magnitude of the absolute acceleration of the main body?
Options
- A.
- B.
- C.
\omega^2 R
- D.
\omega^2 (R + 4L)
Check Your Answer
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
Centripetal Acceleration Vector|Geostationary Satellite Constraints|Vector Cross-Products
Why This Question Is Tricky
Common Mistakes
This question tests the student's ability to distinguish between the kinematics of the center of mass (CoM) and the individual components of a non-rigid system.
A common trap is assuming the main body itself follows the unperturbed geostationary orbit, leading to an acceleration of simply .
Another frequent error is failing to correctly apply the mass ratio when finding the position of the main body relative to the CoM, or forgetting to square the angular velocity factor when differentiating the rotating vector .
By forcing the analysis into the inertial frame, it evaluates the correct superposition of the CoM's centripetal acceleration and the internal rotational acceleration.
Quick Facts About This Question
Question Information
| Subject | Physics |
| Chapter | Motion in a Plane - Class 11 Part 1 |
| Concept | Centripetal Acceleration Vector |
| Difficulty | 8 |
| Cognitive Load | 7 |
| Target Solve Time | 160 sec |
| Access | Free |