Gravitational Field Intensity - Practice Questions & MCQ

• Gravitational field-

It is space or surrounding in which a material body feels the gravitational force of attraction.

• Gravitational field Intensity-

It is the force experienced by a unit mass at a point in the field.

It is denoted by I

If the mass of a body is m then I is given by

 

1.  It is a vector quantity

2.   If the field is produced by a body M the direction of its Gravitational field Intensity is always towards the center of gravity of M.

3. 

4. 

• Gravitational field due to Point mass

 If the point mass M is producing the field and test mass is at distance r as shown in fig

So Force is given as

And the corresponding I is given by 

Where

1.  

Means As the distance (r) of test mass from point (M) Increases I decreases.

2. 

• Superposition of Gravitational field

The net Intensity at a given point due to different point masses (M₁,M₂,M₃…) can be calculated  by doing the vector sum of their individual intensities 

 

• Point of zero intensity-

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

And P is the point where net Intensity==0

Then P is the point of zero intensity

Let point P is at distance x from m1

Then For point P =0

Then

And

 

• Gravitational field line-

          Field line of Isolated mass-

        

Field lines are radially Inward 

As   

 

So we can say that the intensity of the gravitational field at a point P in the field of Isolated mass is equal to the acceleration of test mass placed at that point P.

Properties of Gravitational field line-

1. The line includes arrows which represent the direction of the gravitational field.

2. The magnitude of the gravitational field is proportional to the number of field lines crossing a unit area perpendicular to them.

Value of g is larger when lines are close together

While Value of g smaller when they are far apart

3. The lines never cross

4. Lines do not form closed loops

For Uniform circular ring

At the center of ring 

At a point on its Axis

Where,

 The distance of the point P along the Axis of the ring, from its center .

a= radius of the ring

For Uniform disc

 

 

 Angle with axis

 Radius of disc

At the center of the disc 

At a point on its axis

For Spherical shell

 Radius of shell

 Position of Pt.

 Mass of spherical shell

• Inside the surface 

  

• on the surface

•                Outside the surface

       

For  Uniform solid sphere-

•  Inside surface 

 

• on the surface

• Outside surface