Gravitation is the force of attraction between any two objects with mass or energy. This is a natural phenomenon. It is the gravitational force that brings planets, stars and galaxies together. The tides in the ocean are caused due to the gravitational force of attraction of the moon. The weight of physical objects on earth is given as the product of its mass and the acceleration due to the gravity of the Earth.

Gravitation Formulas for JEE

1. Gravitational Force

According to Newton’s Law of gravitation, the force between two point masses is given by

F= Gm₁m₂/r²

G is the gravitational constant

The direction of the force will be an attraction

2. Gravitational Potential

i) For Point Charge:

V = -GM/r

ii) For circular ring

x is the radius of the ring

R is the distance from the ring

iii) For thin circular disc

iv) Uniform thin spherical shell

V_out = -GM/r

V_surface= -GM/R

V_in = -GM/R

3. Gravitational acceleration

g = GM/R²

4. Variation of g with depth

g_inside≈ g(1-h/R)

5. Variation of g with height

g_outside ≈ g(1-2h/R)

6. Effect of non-spherical earth shape on g

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

7. Effect of earth rotation on apparent weight

mg’_θ = mg = mω²Rcos²θ

8. Orbital velocity of the satellite

9. Escape velocity

10. 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

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Gravitation