## Unit – II A |

## Concept of Acceleration Due To Gravity:

- When a body is released from a height, it gets accelerated towards the earth with constant acceleration, this constant acceleration is called the acceleration due to gravity

### The expression for acceleration due to gravity on the surface of the earth:

–

- Let us consider a body of mass ‘m’ be at rest on the surface of the earth on which the acceleration due to gravity is ‘g’. If ‘M’ and ‘R’ are mass and radius of earth respectively Then by Newton’s law of gravitation the force of attraction between the body and earth is given as

- This force of attraction is equal to weight ‘mg’ of the body

This is the expression for acceleration due to gravity on the surface of the earth.

#### Note:

- Above relation is also used as GM = R²g

### Characteristics of Acceleration Due to Gravity:

- The acceleration due to gravity is on account of the gravitational force acting on the body.
- At given place, the value of acceleration due to gravity is the same for all bodies irrespective of their masses.
- The acceleration due to gravity changes from place to place. i.e. it changes with the change in latitude or altitude or depth.
- Average acceleration due to gravity on the surface is different for different planets.

### Difference Between Acceleration due to gravity (g) and Acceleration due to gravity (g):

- The universal gravitational constant ‘G’ must not be confused with acceleration due to gravity ‘g’.
- ‘G’ is a scalar quantity while ‘g’ is a vector quantity.
- ‘G’ is universal constant, while ‘g’ changes from place to place and from planet to planet.
- Dimensions of ‘G ‘are [M
^{-1}L^{3}T^{-2}], while dimensions of ‘g’ are [M^{0}L^{1}T^{-2}].

### The expression for acceleration due to gravity At a Height ‘h’ From the Surface of the Earth:

- Let us consider a body of mass ‘m’ at rest at height ‘h’ from the surface of the earth. Let the acceleration due to gravity at this height be is ‘g
_{h}’. Let ‘r’ be the distance of the body from the center of the earth. If ‘M’ and ‘R’ are mass and radius of earth respectively then r = R + h. - By Newton’s Law of gravitation, the force of attraction between the body and earth is given as

- This force of attraction is equal to the weight ‘mgh’ of the body at height ‘h’ from the surface of the earth.

This is the expression for the acceleration due to gravity at height h from the surface of the earth.

#### Note:

- Above relation is also used as GM = r² g
_{h}

### The relation between g and g_{h}:

This equation gives the relation between ‘g’ and ‘g_{h}’.

### Notes:

- The value of acceleration due to gravity at the sea level and latitude 45° is taken as the standard.
- The value of acceleration due to gravity at the equator is 9.7804 m/s2 and at poles is 9.8322 m/s² .
- Unless otherwise stated, the value of ‘g’ is taken as 9.81 m/s2 in S.I. system and 981 cm/s².
- The values of ‘g’ for Delhi, Kolkata, and Mumbai are 9.7914 m/s², 9.7876 m/s², 9.7863 m/s² respectively.

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