Gravity Formula

We know gravity is the fundamental force and is the elemental concept of Physics. Gravity or gravitational force is the contribution of the great scientist Sir Isaac Newton. We know that dropping an apple from a tree was the reason for the inception of the Law of Universal Gravitation. In this session, let us learn about the gravity formula and its application.

Gravity or Gravitation Formula

Gravity also termed as gravitation, is a force that occurs among all material objects in the universe. For any two objects or units having non-zero mass, the force of gravity has a tendency to attract them toward each other. Newton’s Law of Universal Gravitation states that:

“Every particle attracts every other particle in the universe with force directly proportional to the product of the masses and inversely proportional to the square of the distance between them”.

If the distance between two masses m1 and m2 is d, then the gravity formula is articulated as:

$F=\frac{Gm_{1}m_{2}}{r^{2}}$

Where,

• G is a constant equal to 6.67 × 10-11 N-m2/kg2
• m1 is the mass of the body 1
• m2 is the mass of body 2
• r is the radius or distance between the two bodies

The gravitational force formula is very useful in computing gravity values, larger mass, larger radius, etc.

Gravity Problems Solved Examples

Underneath are given some questions on gravity which helps one to comprehend the use of this formula.

Problem 1: Calculate the force due to gravitation being applied on two objects of mass 2 Kg and 5 Kg divided by the distance 5cm?

Given: Mass m1 = 2 Kg,
Mass m2 = 5 Kg,
Gravitational Constant G = 6.67 ×× 10-11 Nm2/Kg2

$The\;force\;due\;to\;gravity\;are\;given\;by\;formula\;F=\frac{Gm_{1}m_{2}}{r^{2}}$

F =$\frac{6.67\times 10^{-11}\times 2\times 5}{(5\times 10^{-2})^{2}}$

$=2.668\times&space;10^{-7}N$
Problem 2. What is the magnitude of the gravitational force between the earth and a 1 kg object on its surface? (Mass of the earth is

$$\begin{array}{l}6*10^{24}\end{array}$$
kg and radius of the earth is
$$\begin{array}{l}6.4*10^{6}\end{array}$$
).

From Newton’s law of gravitation, we know that the force of attraction between the bodies is given by

$$\begin{array}{l}F=\frac{Gm_{1}m_{2}}{r^{2}}\end{array}$$
Where,

• m1=
$$\begin{array}{l}6*10^{24}\end{array}$$
kg
• m2 = 1 kg
• r =
$$\begin{array}{l}6.4*10^{6}\end{array}$$
• Substituting in the above equation,

$$\begin{array}{l}F=\frac{6.67*10^{11}(6*10^{24})*1}{(6.4*10^{6})^{2}}\end{array}$$
=9.8 N
This shows that the earth exerts force 9.8 N on a body of mass of 1 Kg.

See the video below, to understand what is gravitation and gravity formula explanation.

Hope you learned the gravity formula along with the law of universal gravitation. For more such valuable equations and formulas stay tuned with BYJU’S!!

Q1

Who put forth the Law of Universal Gravitation?

The Law of Universal Gravitation was put forth by Sir Isaac Newton.

Q2

State law of universal gravitation.

The law of universal gravitation states that:

Every particle attracts every other particle in the universe with force directly proportional to the product of the masses and inversely proportional to the square of the distance between them.
Q3

Write gravity formula.

Gravity formula:
$$\begin{array}{l}F=\frac{Gm_{1}m_{2}}{r^{2}}\end{array}$$

Where,
G is a constant equal to 6.67 × 10-11 N-m2/kg2
m1 is the mass of the body 1
m2 is the mass of body 2
r is the radius or distance between the two bodies

Q4

What is the value of the gravitational constant?

The value of the gravitational constant is
$$\begin{array}{l}6.67*10^{-11} Nm^{-2}/kg^{2}\end{array}$$
.
Q5

True.