Question

Find the gravitational force between the earth and an object of 2 kg mass placed on the surface. (Given mass of the earth $6 \times {10^{24}}$kg and radius of the earth= $6.4 \times {10^6}$ m)

Answer 1

Hint: Basically there are four fundamental forces in nature. They are gravitational force, electrostatic force, strong nuclear force, weak nuclear force. Here the force in action is gravitational force and it is a long range force and the weakest of the four fundamental forces.

Formula used:
$F = \dfrac{{GMm}}{{{R^2}}}$

Complete step by step answer:
Gravitational force will be acting between any two masses at a particular distance. Since the magnitude of that force is very small nobody feels it. There are some similarities between the gravitational force and electrostatic force. gravitational force acts between the two masses whereas electrostatic force acts between the two charges. Both follow the inverse square law which means that the force will be inversely proportional to the square of distance between them.
So Newton discovered this gravitational force and due to this everybody on the earth is acted upon by the force due to the earth and this is what we call as the weight of the body.
We have the expression for the force between earth of mass ‘M’ and body of mass ‘m’ which are separated at the distance ‘r’ from the center of the earth
That expression is
$F = \dfrac{{GMm}}{{{R^2}}}$
Where ‘G’ is the gravitational constant.
Value of G is $6.7 \times {10^{ - 11}}$ and the value on M is $6 \times {10^{24}}$ kg and the value of ‘r’ here is nothing but the radius of the earth as mass m=2kg is kept on the surface of the earth. The radius of earth is $6.4 \times {10^6}$ m
By substituting all these values in the formula we get force as
$F = \dfrac{{GMm}}{{{R^2}}}$
$\eqalign{
  & \Rightarrow F = \dfrac{{6.7 \times {{10}^{ - 11}} \times 6 \times {{10}^{24}} \times 2}}{{{{(6.4 \times {{10}^6})}^2}}} \cr
  & \Rightarrow F = 19.6N \cr} $
Hence 2kg mass will experience 19.6N of force.

Note:
The nature of the gravitational force is always attractive. In case of electrostatic force the constant will be of higher magnitude but here in gravitation the gravitational constant is of very low magnitude and this is the reason why gravitational force is the weakest force of all.