- Books Name
- Science Made Easy Science Book

- Publication
- Science Made Easy

- Course
- CBSE Class 9

- Subject
- Science

**Gravitational Acceleration and its value at the surface of earth**

**→** The uniform acceleration produced in a freely falling object due to the gravitational force of

earth, is called acceleration due to gravity.

→ It is represented by ‘g’ and it always acts towards the centre of the earth.

**Mathematical Expression for ***g*

From the second law of motion, force is the product of mass and acceleration.

**F**** =** *ma*

For free fall, acceleration is replaced by acceleration due to gravity.

Therefore, force becomes:

**F**** = ***mg *….(i)

**But from Universal Law of Gravitation,**

**Factors Affecting the Value of g**

- As the radius of the earth increases from the poles to the equator, the value of
*g*becomes greater at the poles than at the equator. - As we go at large heights, value of
*g*decreases.

**To Calculate the Value of g**

Value of universal gravitational constant, *G* = 6.7 × 10–11 N m2/ kg2,

**Mass of the earth, M =** 6 × 1024 kg, and

**Radius of the earth, R =** 6.4 × 106 m

**Putting all these values in equation** (iii), we get:

Thus, the value of acceleration due to gravity of the earth, g = 9.8 m/s^{2}.

**Difference between Gravitation Constant (G) and Gravitational Acceleration (g)**

**Motion of Objects Under the Influence of Gravitational Force of the Earth**

Let an object is falling towards earth with initial velocity *u*. Let its velocity, under the effect of gravitational acceleration *g*, changes to *v* after covering the height *h* in time *t*.

**Then the three equations of motion can be represented as:**

Velocity (*v*) after *t *seconds, *v *= *u *+ *ght*

Height covered in *t *seconds, *h *= *ut* + ½*gt ^{2}*

Relation between

*v*and

*u*excluding

*t*,

*v*=

^{2}*u*+ 2

^{2}*gh*

The value of

*g*is taken as positive in case of the object is moving towards earth and taken as negative in case of the object is thrown in opposite direction of the earth.