Relation Between Gravitational Field And Potential - Practice Questions & MCQ

Gravitational field and potential are related as

Where E is Gravitational field

And V is Gravitational potential

And r is the position vector 

And Negative sign indicates that in the direction of intensity the potential decreases.

Then

Proof-

Let gravitational field at a point r due to a given mass distribution is E.

If a test mass m is placed inside a uniform gravitational field E.

Then force on a particle m when it is at r is  as shown in figure

As the particle is displaced from r to r + dr the

work done by the gravitational force on it is

The change in potential energy during this

displacement is

And we know that Relation between Potential and Potential energy

As

So

Integrating between r₁, and r₂

We get

If r₁=r₀, is taken at the reference point, V(r₀) = 0. 

Then the potential V(r₂=r) at any point r is 

in Cartesian coordinates, we can write

Then

So  

If y and z remain constant, dy = dz = 0

Thus

Similarly