If “a” is the major axis and “b” the minor axis then the orbit is circular if – Free B11
Answer
Planetโs Orbital Motion โ Central Force Motion Explained
4. Orbit Shape and Circular Condition
An elliptical orbit is a slightly elongated circle (oval-shaped). For the orbit to be perfectly circular:
- It must satisfy: a = b, where:
- a = semi-major axis
- b = semi-minor axis
- Thus, when a = b, the orbit is circular.
Correct Option: (b)
5. Effective Mass in Two-body Central Force Systems
When two objects of mass mโ and mโ interact under a central force, we use the concept of reduced mass:
- Reduced mass formula: ฮผ = (mโ ร mโ) / (mโ + mโ)
- This allows simplifying the system to a single-body problem.
Correct Option: (d)
6. Focus of Elliptical Orbits in Two-body Systems
In an elliptical orbit, there are always two foci:
- In a reduced mass system, the heavier mass occupies one focus.
- The lighter mass orbits this focus along the elliptical path.
Correct Option: (b)
7. Total Energy in Elliptical Orbit
For a particle moving in an elliptical orbit under a central force:
- Total energy (E) = Kinetic Energy (KE) + Potential Energy (PE)
- At point A: KE > PE
- At point B: PE > KE
- But total energy remains constant: EA = EB
Correct Option: (b)
8. Angular Momentum Conservation
In absence of external torque, angular momentum stays constant:
- LA = LB
- This conservation is fundamental in central force systems.
Correct Option: (b)
โ Summary of Correct Answers
| Question Number | Correct Option |
|---|---|
| 4 | (b) |
| 5 | (d) |
| 6 | (b) |
| 7 | (b) |
| 8 | (b) |
๐ More Examples for Particle Motion
- The figure gives a plot of potential energy versus position along an x axis
- Sammy is talking to Sally. Position A is a position in front of Sammyโs mouth
- Consider a particle moves in inverse square law central force motion and