Question

Define acceleration due to gravity. Deduce an expression for it in terms of the mass of the earth (M) and the universal gravitational constant ‘G’.

Answer 1

1. Definition: Acceleration due to gravity is the acceleration gained by an object because of gravitational force. Its unit is $m/s^2$.

Step 1

As we know,$F=ma$ ,…………(1)

where, 'm' is mass of body

‘a’ is acceleration

Step 2

The gravitational force acting on a mass ‘m’ on earth's surface is

$F=GMm/R^2$

$F=m\times GM/R^2$……………….(2)

Step 3

On comparing equation 1 with equation 2 we get,

$a=GM/R^2$

Here, $a=g$ .

As we know, from the definition of acceleration due to gravity

$a=g=GM/R^2$