# Gravitational Field

The space around an object within which its force of gravitation is experienced is termed as gravitational field.

### Gravitational Field Strength or Intensity:

The gravitational field intensity at a point is described as the force experienced by a unit mass located at that point.

### Intensity of the field felt by a test mass:

Let M be the mass of an object around which a gravitational field occurs. Let m be a test mass located in this field. The test mass is so selected that it does not influence the gravitational field. The arrow over $$\overrightarrow{E}$$ specifies it is a vector quantity, although mass is a scalar unit.

A force $$\overrightarrow{F}$$ field is the force felt by the unit mass m. The strength $$\overrightarrow{E}$$ of the field is the force felt by the unit mass.

$$\Rightarrow \overrightarrow{E} = \frac {\overrightarrow{F}}{m}$$

$$\overrightarrow{E}$$ is a ventor quantity. It is directed towards M.

$$\Rightarrow \overrightarrow{E} = \frac{\overrightarrow{F}}{m} = \frac{m.\overrightarrow{a}}{m} = \overrightarrow{a}$$

If the test mass m were free to move, it would move with acceleration towards M. Therefore, $$\overrightarrow{a}$$ is the free acceleration.

The intensity is described as the free acceleration experienced by a trial mass at that point.

### Units Of Gravitational field: The units in the

• The C.G.S. system is dyne gm-1 or cms-2
• SI system is Nkg-1 or ms-2

If M is the mass of the Earth, then $$\vec{E}=\frac{m\vec{g}}{m}=\vec{g}$$ , acceleration due to gravity.

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#### Practise This Question

In an amplitude modulated wave for audio frequency of 500 cycle/second, the appropriate carrier frequency will be