3. Weight and Mass

^{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/s².