# Important Gravitation Formulas for JEE

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## What is Gravitation?

Gravity, also called gravitation, is the universal force of attraction that is acting upon all the matters present in the Earth. It was founded by Isaac Newton. It is considered as a natural phenomenon due to which all things with mass or energy, including planets, stars, galaxies, and even light are attracted to one other. Earth’s gravity determines the weight of all the physical objects, but the moon’s gravity is the cause of ocean tides. In simple words, it is the force of attraction that the bodies of different objects exert on one another because of their masses. The SI unit of gravitation is kilogram - weight. Students generally learn all this in the JEE Mains physics gravitation chapter.

### What is Gravitational Force?

The gravitational force is a force that causes attraction between any two objects having a certain amount of mass. People usually call gravitational forces attractive because it is always engaged in pulling masses to one another but never pulls these masses apart from each other. This proves the fact that every object, including us, is pulling every other object that is present in the universe.

### Properties of Gravitational Force

The properties of gravitational force are:

• The gravitational force is considered as a long-range force that exists between two objects without considering the medium that separates them.

• The gravitational force is directly proportional to the product of the mass of the two objects. This states that an item with a larger mass will yield a larger force.

• The force follows the inverse square law. The gravitational force is inversely proportional to the square of the distance between the two objects, larger the distance less the force.

• On the surface of the Earth, the gravitational force produces a constant acceleration that is calculated to be g= 9.8 m/s2.

• The gravitational force has always been a force of attraction that always attracts two objects together and never pulls them apart from each other.

• The gravitational force is always independent of the separating medium.

• Among the four fundamental forces, the gravitational force is the weakest of them all.

• The gravitational force always acts along the line which joins the center of the two objects, which is why it is called the central force.

• The gravitational force is directly proportional to the weight of the objects.

• The gravitational force also acts even if the objects are not in physical contact.

All these properties are taught in the JEE Mains physics gravitation chapter.

• Gravity causes waterfalls, that helps us to generate electricity.

• Gravity also causes rain which is required to balance the Earth's environment for living beings.

• Earth's gravity can pull large rocks from space known as asteroids. If these asteroids enter into the Earth's atmosphere, they can be the reason for substantial catastrophic damage. Large asteroids are attracted more due to their masses, and they also cause more damage.

• Gravity causes the fall of an object from higher altitudes that can cause many fatal accidents for humans.

### Important Gravitational Formulas

Gravitation all formulas are as follows.

1. Gravitational Force

F = Gm₁m₂ / r2

G is the gravitational constant.

The direction of the force will act as an attraction.

1. Gravitational Potential

i) For Point Charge:

V = -GM /r

ii) For Circular Ring

V = -GM / ($\sqrt{R^{2}}$ + x2)

iii) For thin circular disc

V = -2GM / R2( $\sqrt{R^{2} + x^{2}}$ - x )

iv) Uniform Thin Spherical Shell

Vout  = -GM / r

Vsurface = -GM / R

Vin = -GM / R

1. Gravitational Acceleration

g = GM / R2

1. Variation of g With Depth

ginside ≈ g[(1 - h) / r]

1. Variation of g With Height

goutside ≈ g[(1 - 2H) / R]

1. Effect of Non - Spherical Earth Shape on g

G at pole > g at the equator ( since Re - Rp ≈ 21km)

1. Effect of Earth Rotation on Apparent Weight

mg’θ = mg = mw2Rcos2θ

1. Orbital Velocity of the Satellite

V₀ = $\sqrt{GM/R}$

1. Escape Velocity

Vℯ = $\sqrt{2GM/R}$

1. 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

All these important formulas can be learned from the gravitation chapters.

### Solved Example:

Example 1:

What is the force of the gravity that is acting on an object present in the Earth’s surface? Earth’s mass = 5.98 x 1024 kg, object’s mass = 103 kg, radius of the Earth = 6.38 x 106 m.

Solution:

F = Gm₁m₂ / r2 = [(6.67 x 10-11)  (5.98 x 1024)(103)]/ (6.38 x 106)2