Gravity Formula Physics

Gravity is the force that attracts two bodies towards each other. This is the force that causes apples to fall towards the ground on the hand due to these planets are orbiting the sun. The object with more mass will have a stronger gravitational pull. It is one of the four fundamental forces available in nature. Although nobody has discovered gravity exactly, the legend and famous astronomer Galileo Galilei did some of the earliest experiments with it. As he dropped the balls off the Tower of Pisa to see how fast they fell. This article will explain the concept of interesting gravity and gravity formula physics with examples. Let us learn it!

What is Gravity?

Gravity is also popular as gravitation. It is the force that occurs among all material objects in the universe. For any two objects with some mass, the force of gravity has a tendency to attract them towards each other. This fact is according to the Universal Law of Gravitation. It is what causes the objects to have weight on the earth. When we weigh ourselves, the scale tells us how much gravity is acting on our bodies.

Historically, philosophers such as Aristotle thought that heavier objects always accelerate towards the ground with ore faster speed. But later experiments disproved it. Because acceleration due to gravity is always a constant and is not depending on the mass of the falling object.

Source: en.wikipedia.org

The Formula for Gravity

Isaac Newton gave his Theory of Universal Gravitation in the 1680s. He found that gravity acts on all kinds of objects and it is a function of both mass and distance. Every object attracts the other one with a force which is proportional to the product of their masses. And also it is inversely proportional to the square of the distance between them. The equation is represented as:

\(F_{g} = G \frac {(m_{1} \times m_{2})} { r^{2}}F_{g}\)

Where,

\(F_{g}\)	Gravitational force
G	Universal gravitational constant
\(m_{1} and m_{2}\)	the masses of the two objects
r	Distance between them

Value of G is \(6.67 \times 10^{-11} N-m^{2} kg^{-2},\) This equation works extremely well to predict how objects such as planets in the solar system behave.

Solved Examples for Gravity Formula Physics

Q.1: What will be the gravitational force acting upon two objects of the masses 15 g and 15 kg. These are kept at 11 m distance. Use Gravity Formula Physics

Solution: Given parameters are,

• Gravitational constant, \(G = 6.67 \times 10^{-11} N-m^{2} kg^{-2},\)
• \(M_{1}  = 15 g = 0.015\) kg
• \(M_{2} = 15 \)kg
• r = 11 m.

Now the formula is: \(F_{g} = G \frac {(m_{1} \times m_{2})} { r^{2}}\)

Substituting the values, We have

\(F_{g} = 6.67 \times 10^{-11} \times \frac {(.015 \times 15)} { 11^{2}}\\\)

\(F_{g} = 1.24 \times 10^{-13} N\)

Therefore, the gravitational force will be \(1.24 \times 10^{-13} N.\)

Q. 2: If the gravitational force between two objects is equal to \(1.1 \times 10^{-11} N\). If both the masses are 6 kg each. Then determine the distance between them.

Solution:  The force, \(F_{g} = 1.1 \times 10^{-11} N.\)

\(M_{1} =  m_{2}=  6 kg.\)

Formula is: \(F_{g} = G \frac {(m_{1} \times m_{2})} { r^{2}}\)

Rearranging it: \(r^{2} =  G \frac {(m_{1} \times m_{2})} { F_{g}}\\\)

Substituting the values,

\(r^{2} = 6.67 \times 10^{-11} \times \frac {6 \times 6}{1.1 \times 10^{-11}}\\\)

\(r = 14.69 \;m\)

Thus distance will be 14.69 m