Gravitational Field, Gravitational Potential & Gravitational Potential Energy (B.Sc Physics)

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Gravitational Field :

The space/region around a body within which its gravitational force of attraction can be felt is called as gravitational field.

As we know that gravitational field of earth exist, similarly gravitational field exist for all the bodies having masses. Since this is an attractive force, so attracts other masses. The gravitational field is a vector field.

Gravitational Field Intensity(E):

The gravitational field intensity at a point inside the attractive gravitational filed is defined as the force experienced by a unit mass placed at that point.

It is defined as, E= -Gm/r2. The negative sign indicates that the force is attractive.

Gravitational Potential (V):

The work done in moving a unit mass body from infinity to any point in the gravitational field of a body is called the gravitational potential at that point.

Gravitational Potential due to a Point Mass:

    Let a body of mass m is placed at point 'A' & 'P' is an observation point situated at a distance 'r' inside the gravitational field of the body. Let a unit mass object m0= 1 is placed at infinity & brought form infinity to point 'P'.

    Let B is a point situated a ta distance 'x' from the body of mass 'm'. When m0 is placed at 'B', the force between m & m0 is

The negative sign is the indication of the attractive nature of gravitational force.

Relation between Gravitational Potential & Field:

Let V= Gravitational Potential at P.

r= Distance of the observation point, so 

Gravitational Potential Energy:
Gravitational potential energy of a system of masses is defined as the total work done in bringing all the masses from infinity to their respective places & assembling together.

For a system of two masses:

 

Let us consider two bodies having masses m1 & m2 are separated by a distance 'r' & placed at points 'A' & 'B' respectively. Let us consider that both were placed at infinity originally.

    Firstly the body m1 was brought from infinity to point 'A' & at that time there were no other masses & not their gravitational field, hence no force acts on m1, so no work is done in placing m1 from infinity to the point 'A'.

    so w1=0 --------------------------------(1)

Secondly when the body m2 brought from infinity to the point 'B' & already m1 was present there & m2 is influenced by the gravitational field of m1.So some force acts on m2.

    Let 'C' is point at a distance 'x' from the point 'A'. When m2 was at 'C', the force between m1 & m2 is 

For a system of three masses:

Numerical:

Q1: Three bodies of masses 20kg each are placed at the three corners of an equilateral triangle of side 20m. Find the gravitational potential energy of the system ?

Ans: 

Q2: Four bodies of masses 20kg each are placed at the four corners of a square of side 20m. Find the gravitational potential energy of the system?

Ans:

Short Answer Type:

Q1: The maximum value of gravitational potential energy is __________.

Ans: Zero

Q2: The force of gravity is not a conservative force?

    a) True    b) False

Ans: False

Q3: Gravitational potential energy can be zero but gravitational potential can never be zero.            

    a) True    b) False

Ans: False

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