Can you derive acceleration due to …

According to the second law of motion, force is the product of mass and acceleration. Suppose the mass of the stone be m. The acceleration involved in falling objects due to the gravitational force and is denoted by g.

Therefore the magnitude of the gravitational force F will be equal to the product of mass and acceleration due to the gravitational force, that is,

F = m g                                                                                                           ii.

From Eqs. i. and ii.  we have

m g = G M x m/d²

Or g = GM /d²

where M is the mass of the earth, and d is the distance between the object and the earth.

Let an object be on or near the surface of the earth. The distance d will be equal to R, the radius of the earth. Thus, for objects on or near the surface of the earth,

mg = = G M x m/r²

g = GM /r²

To Calculate the Value of g:

To calculate the value of g, we should put the value of universal gravitational constant, G = 6.673 × 10^–11 N m² kg^–2; mass of the earth, M = 6 x 10²⁴ kg; and radius of earth R = 6.4 x 10⁶ m in the given equation:

g = GM /r²

g = 6.673 × 10^–11 N m² kg^–2 x 6 x 10²⁴ kg/(6.4 x 10⁶ m)² = 9.8 m/s²

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