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Gravitational Acceleration Formula

Gravity, also called gravitation,  in mechanics, the universal force of attraction acting between all matter. Gravity is a force that exists between the Earth and the objects that are near it. On Earth all bodies have a weight, or downward force of gravity, proportional to their mass, which Earth’s mass exerts on them. Gravity is measured by the acceleration that it gives to freely falling objects.

Gravity causes a body to accelerate. The acceleration with which a body moves when given a free fall is called acceleration due to gravity.The gravitational acceleration formula is given by
Gravitational Acceleration Formula
Where,
G = Universal gravitational constant,
M = mass of the planet,
r = radius of the planet

This formula is used to find the acceleration due to gravity anywhere on the earth. If you know some of the quantities in the above formula you can get to know the unknown quantity. The acceleration due to gravity on earth is 9.8 m/s2.

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Gravitational Acceleration Examples

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Lets go through some gravitational acceleration examples:

Solved Examples

Question 1: Calculate the acceleration due to gravity on the moon surface (mass of the moon M = 7.4 $\times$ 1022 kg, radius of moon r = 1.74 $\times$ 106 m)
Solution:
 
Given : Mass of moon M = 7.4 $\times$ 1022 kg, radius of moon r = 1.74 $\times$ 106 m
Acceleration due to gravity is
ag = $\frac{GM}{R^2}$
$\therefore$ ag = $\frac{6.67 \times 10^{-11}Nm^2/kg^2 \times 7.4 \times 10^{22} kg}{(1.74 \times 10^6)^{2}}$
         = 1.63 m/s2.
 

Question 2: By what ratio the acceleration due to moon varies with earth?
Solution:
 
We know acceleration due to gravity on earth = 9.8 m/s2 and acceleration due to gravity on moon = 1.63 m/s2

$\therefore$ $\frac{a_{g\ on\ moon}}{a_{g\ on\ earth}}$

= $\frac{1.63\ m/s^2}{9.8\ m/s^2}$

  = $\frac{1}{6}$

The acceleration due to gravity ratio varies by $\frac{1}{6}$
 

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