Important Gravitation Formulas For JEE
Gravitation is one of the fundamental forces of nature that governs the motion of celestial bodies, planets, stars, and everything with mass. Understanding the principles of gravitation is crucial for students preparing for the Joint Entrance Examination (JEE) or any other competitive examination that involves physics. In this article, we will explore important gravitation formulas that are essential for JEE aspirants.
For the Joint Entrance Examination (JEE) and other competitive exams, it's essential to have a solid understanding of gravitation and the relevant formulas. Here are some important gravitation formulas you should be familiar with:
Universal Gravitational Constant (G):
- This constant relates the force of gravitational attraction between two objects with their masses and the distance between them.
Gravitational Force (F):
- The force of attraction between two objects due to gravity.
Where:
F is the gravitational force.
G is the universal gravitational constant.
M1 and m2 are the masses of the two objects.
r is the distance between the centers of the two objects.
Gravitational Field Strength (g):
- The gravitational force per unit mass experienced by an object in a gravitational field.
Where:
g is the gravitational field strength.
F is the gravitational force.
m is the mass of the object
Gravitational Potential Energy (U):
- The energy associated with the position of an object in a gravitational field.
Where:
U is the gravitational potential energy.
G is the universal gravitational constant.
m1 and m2 are the masses of the two objects.
r is the distance between the centers of the two objects.
Escape Velocity (v_e):
- The minimum velocity required for an object to escape the gravitational pull of a celestial body.
Where:
Ve is the escape velocity.
G is the universal gravitational constant.
M is the mass of the celestial body.
r is the distance from the center of the celestial body to the object.
Gravitational acceleration
g = GM/R2
Variation of g with depth
ginside≈ g(1-h/R)
Variation of g with height
goutside ≈ g(1-2h/R)
Effect of non-spherical earth shape on g
g at pole ＞ g at the equator (since Re – Rp ≈ 21km)
Effect of earth rotation on apparent weight
mg’θ = mg = mω2Rcos2θ
Orbital velocity of the satellite
Kepler’s Law
First law: Elliptical orbit with the sun at one of the focus
Second Law: Areal velocity is constant (dA/dt =0)
Third Law: T2 ∝ R3
Gravitation is a fundamental concept in physics that underpins our understanding of the universe. For JEE aspirants, mastering the important gravitation formulas is not only essential for acing the exam but also for comprehending the intricate mechanics of celestial bodies and everyday phenomena. By grasping these formulas and their applications, you can confidently tackle gravitation-related questions in your JEE examination and develop a deeper appreciation for the force that governs our cosmos.
Important Gravitation Formulas For JEE FAQs
Q1. What is escape velocity (v_e), and how is it relevant to JEE?
Ans. Escape velocity (v_e) represents the lowest velocity an object must attain to overcome the gravitational influence of a celestial body. It's relevant for understanding space exploration and satellite launch calculations, which can be tested in JEE.
Q2. Are these formulas applicable only to Earth or any celestial body?
Ans. These gravitation formulas are universal and can be applied to any celestial body. The values of constants like 'G' might change depending on the body, but the formulas themselves remain the same.
Q3. How can I practice and master these formulas for the JEE?
Ans. To excel in JEE, practice is key. Solve a variety of problems related to gravitation, and make sure you understand the underlying concepts. You can also seek guidance from teachers, coaching classes, or online resources to clarify doubts.
Q4. Are these gravitation formulas sufficient for JEE, or should I study additional topics?
Ans. While these gravitation formulas are essential, the JEE syllabus covers a wide range of physics topics. Having a thorough comprehension of all pertinent subjects is imperative for achieving success in the examination.
Q5. Where can I find practice questions and mock tests related to these gravitation formulas for JEE preparation?
Ans. You can find practice questions, mock tests, and study materials in JEE preparation books, online platforms, and coaching institutes. Many websites and apps offer free or paid resources to help you practice and prepare effectively.
