Question

define acceleration due to gravity. derive an expression for acceleration due to gravity in terms of mass of the earth (m) and universal gravitational constant (g)

Answer 1

The acceleration due to gravity near the earth's surface is g = $\bold {\frac {GM_e} {R_e {} ^{2} } }$

The direction of this acceleration is vertically downwards, that is, towards the earth's centre.

The acceleration of a body moving near the earth's surface under the influence of gravity is the same regardless of weather it moves up, falls down or moves at some angle to the vertical.

Answer 2

Acceleration due to gravity can be represented as follows.

Given:

Mass of Earth= m

Universal gravitational constant= g

To Find:

Expression for acceleration due to gravity.

Solution:

Acceleration due to gravity can be defined as the acceleration produced in an object due to the gravitational force of the earth.

The force acting on a body due to gravity is given by-

F=m'g (1)

The Universal law of Gravitation states that f=Gm'm/r² (2)

Here, f= force between two bodies; g= universal gravitational constant; m'= mass of body; m= mass of earth; r= radius of earth.

On equating (1) and (2),

m'g = Gm'm/r²

Since mass of the object (m') is constant,

g = Gm/r²

Hence, the expression for acceleration due to gravity is g = Gm/r²