2024P2Q2 | ORBITAL DYNAMICS | GRAVITATION | MECHANICS | JEE ADV 2024 | TACHYON PHYSICS

Q.2 A particle of mass 𝑚 is under the influence of the gravitational field of a body of mass 𝑀 (≫ 𝑚).
The particle is moving in a circular orbit of radius 𝑟0 with time period 𝑇0 around the mass 𝑀. Then,
the particle is subjected to an additional central force, corresponding to the potential energy
𝑉c(𝑟) = 𝑚𝛼/𝑟
3
, where 𝛼 is a positive constant of suitable dimensions and 𝑟 is the distance from
the center of the orbit. If the particle moves in the same circular orbit of radius 𝑟0 in the combined
gravitational potential due to 𝑀 and 𝑉c(𝑟), but with a new time period 𝑇1, then (𝑇1
2 − 𝑇0
2
)/𝑇1
2
is
given by
[𝐺 is the gravitational constant.]
(A) 3𝛼
𝐺𝑀𝑟0
2
(B) 𝛼
2𝐺𝑀𝑟0
2
(C) 𝛼
𝐺𝑀𝑟0
2 (D) 2𝛼
𝐺𝑀𝑟0
2




In this video, we solve a challenging problem involving a particle moving in a circular orbit under the influence of a gravitational field and an additional central force. Learn how to analyze the effects of both gravitational and central forces on the orbital time period, and understand the impact of an additional potential energy term on the motion. We will derive a relation between the initial and modified orbital periods step-by-step."

🌀 What You'll Learn:

How gravitational and additional central forces affect the orbital motion of a particle.
Application of mechanics to derive relationships between potential energy, force, and orbital period.
Step-by-step techniques for solving advanced problems involving combined central forces and gravitational potentials.
✨ Benefits You'll Gain:

Ideal for JEE aspirants aiming to strengthen their understanding of orbital dynamics and central forces.
Learn to apply advanced mechanics concepts to analyze motion under multiple forces.
Gain problem-solving skills to tackle complex gravitational and potential energy questions in competitive exams.
👍 Like this video? Give it a thumbs up and subscribe to Tachyon for more insightful physics tutorials! 🌐 Visit tachyonedu.co.in for additional resources and practice questions.
📞 Contact us: 9010811242
📧 Email: [email protected] for any queries or more information!

🔍 Hashtags: #TachyonPhysics #OrbitalMotion #GravitationalForce #CentralForce #PhysicsMadeSimple #JEEAdvanced #JEEPrepIn this video, we solve a challenging problem involving a particle moving in a circular orbit under the influence of a gravitational field and an additional central force. Learn how to analyze the effects of both gravitational and central forces on the orbital time period, and understand the impact of an additional potential energy term on the motion. We will derive a relation between the initial and modified orbital periods step-by-step."

🌀 What You'll Learn:

How gravitational and additional central forces affect the orbital motion of a particle.
Application of mechanics to derive relationships between potential energy, force, and orbital period.
Step-by-step techniques for solving advanced problems involving combined central forces and gravitational potentials.
✨ Benefits You'll Gain:

Ideal for JEE aspirants aiming to strengthen their understanding of orbital dynamics and central forces.
Learn to apply advanced mechanics concepts to analyze motion under multiple forces.
Gain problem-solving skills to tackle complex gravitational and potential energy questions in competitive exams.
👍 Like this video? Give it a thumbs up and subscribe to Tachyon for more insightful physics tutorials! 🌐 Visit tachyonedu.co.in for additional resources and practice questions.
📞 Contact us: 9010811242
📧 Email: [email protected] for any queries or more information!

🔍 Hashtags: #TachyonPhysics #OrbitalMotion #GravitationalForce #CentralForce #PhysicsMadeSimple #JEEAdvanced #JEEPrep