Gravitational Field Intensity of a Point Mass

Have you ever contemplated why leaves fall on the ground? Why don’t they fly off in the air? The reason is very simple. This phenomenon takes place because of a strong force of attraction. A force that is invisible to the eye but is all around the universe. The force that binds all the masses in the universe together is the Gravitational force. 

Example- Fruits falling from a tree.

Fruits fall on the ground because of the gravitational pull present on Earth.

This force is not only limited to our planet but also holds the entire universe together. This force always tries to keep masses together and never repels them apart.

The work behind the study of gravitational force is dominated by Issac Newton and Albert Einstein.

Gravitational field

The gravitational field is a model that explains the gravitational force per unit mass exerted on a small mass at that point. The space around a massive body in which the gravitational force of that body can be felt is known as the gravitational field. It is the gravitational force or weight acting on a mass m in the gravitational field g.

It is given by-

F= mg

Gravitational field intensity

Gravitational field intensity is simply the strength of the gravitational field. Hence, it is also known as gravitational field strength. The intensity of the gravitational field is the force experienced by unit mass placed at a particular point in the gravitational field.

The variable N/kg denotes the unit of gravitational field intensity. A gravitational force intensity depends on the source mass and the distance of the unit mass from the source mass. 

In any way, if the test mass experiences a force F, then the intensity of gravitational field will be,

I= (GMm/r²) / m

I= (GM)/ r²

In the above formula, r is the distance of point P from the body’s centre producing gravitational force.

Now, let us suppose that if the unit mass m is placed on the surface of the Earth, then the gravitational force acting on the test mass m will be equal to the weight w of this mass.

Now, I= W/m

=mg/m=g

Or, I= g

In the above formula, g is equal to the acceleration of gravity at that point.

Solved examples

Now let us explore this topic with the help of examples:

Question: The gravitational force on a body of mass 2 kg situated at a point is 40 N. Calculate the gravitational field intensity.

Solution: We know that,

I= GM/r²               

And we have also studied that gravitational force is equal to,

F= GMm/r²

So, after doing the gross product, we get that,

Gm/r²= F/M

I = F/M

And according to our question, the force is 40 N & the mass is 2 kg. Now when we put the values in the equation, we will see that,

I = F/M

= 40/2

= 20 N/ kg 

Question: The gravitational force on a body of mass 3 kg situated at a point is 96 N. Calculate the gravitational field intensity at that point.

Solution: We know that,

I= GM/r²               

And we have also studied that gravitational force is equal to,

F= GMm/r²

So, after doing the gross product, we get that,

Gm/r²= F/M

I = F/M

And according to our question, the force is of 96 N & the mass is of 3 kg

Now, when we put the values in the equation, we will see that,

I = F/M

= 96/3

= 32 N/ kg 

Conclusion

Gravity is essential to sustain the planet. The binding force possessed by the gravitational force is the driving force behind the smooth life taking place on the planet. The gravitational field is a model that explains the gravitational force per unit mass exerted on a small mass at that point. Gravitational field intensity is simply the strength of the gravitational field. Gravitational force intensity depends on the source mass and the distance of the unit mass from the source mass. The unit of gravitational field intensity is denoted by the variable N/kg.