Gravitational Potential - Practice Questions & MCQ

In a gravitational field potential V at a point, P is defined as negative of work done per unit mass in changing the position of a test mass from some reference point to the given point.

Note-usually reference point is taken as infinity and potential at infinity is taken as Zero.

We know that

So

And

Gravitational potential

Field Intensity

small distance

We can also write

Means a negative gradient of potential gives the intensity of the field .

The negative sign indicates that in the direction of intensity the potential decreases.

• It is a scalar quantity.

• 

• 

• Gravitational Potential at a distance 'r'

If the field is produced by a point mass then 

So

          

                at      

 

• Gravitational Potential difference

In the gravitational field, the work done to move a unit mass from one position to the other is known as Gravitational Potential difference.

            If the point mass M is producing the field

Point A and B are shown in the figure.

=Gravitational potential at point A

=Gravitational potential at point B

 

    

 

                    the distance of mass at

                   distance of mass at

             =The gravitational potential difference in bringing unit mass m from point A to point B in the gravitational field produced by M.

            

           

 

• Superposition of Gravitational potential

The net gravitational potential at a given point due to different point masses (M₁,M₂,M₃…) can be calculated  by doing a scalar sum of their individuals Gravitational potential.

         

              

           

mass 

distances

 

• Point of zero potential

           Let m₁ and m₂ are separated at a distance d from each other

 

          

And P is the point where net Gravitational potential

Then P is the point of zero Gravitational potential 

Let point P is at distance x from m₁

Then For point P  

               So

For Uniform circular ring

distance from ring

radius of Ring

Potential 

 

At a point on its Axis 

At the center 

For Uniform disc

 

Radius of disc

M-mass of disc

• At the center of the disc 

              

• At a point on its axis

                    

 For Spherical shell

 

Radius of shell

distance from the center of the shell

 

• Inside the surface

          

       

• on the surface

          

       

• Outside the surface 

        

      

 

Uniform solid sphere

Radius of sphere

Mass of sphere

distance from the center of sphere

• Inside the surface 

            

        

• on the surface

        

• Outside the surface

          

• Tip-