Question

Calculate the value of $'g'$ on the surface of the earth. The mass of the earth is $6 \times {10^{24}}\,Kg$ and the radius of the earth is $6 \times {10^6}\,m$ . Gravitational constant is $6.67 \times {10^{ - 11}}\,N{m^2}K{g^{ - 2}}$ .

Answer 1

Hint Use the formula of the acceleration due to gravity and substitute the gravitational constant, mass of the earth and the radius of the earth in it. The simplification of it provides the answer for the acceleration due to gravity of the objects in the earth.
Useful formula:
The formula of the acceleration due to gravity is given by
$g = \dfrac{{GM}}{{{r^2}}}$
Where $g$ is the acceleration due to gravity, $G$ is the gravitational constant, $M$ is the mass of the earth and $r$ is the radius of the earth.

Complete step by step answer
It is given that the
The mass of the earth , $M = 6 \times {10^{24}}\,Kg$
radius of the earth, $r = 6 \times {10^6}\,m$
Gravitational constant, $G = 6.67 \times {10^{ - 11}}\,N{m^2}K{g^{ - 2}}$
Let us consider the formula of the acceleration due to gravity,
$g = \dfrac{{GM}}{{{r^2}}}$
Substitute the gravitational constant, mass of the earth and the radius of the earth in the above formula, we get
$g = \dfrac{{6.67 \times {{10}^{ - 11}}\, \times 6 \times {{10}^{24}}\,}}{{{{\left( {6 \times {{10}^6}\,} \right)}^2}}}$
By performing the various basic arithmetic operations, we get
$g = \dfrac{{6.67 \times {{10}^8}}}{{6 \times {{10}^6}}}$
By further simplification of the above equation, we get
$g = 9.8\,m{s^{ - 2}}$

Hence the acceleration due to gravity of the earth is obtained as the $9.8\,m{s^{ - 2}}$ .

Note The gravitational force of the earth is mainly due to the presence of the molten iron and the nickel in the inner core of the earth. It is constant at all the surface of the earth. As there is the gravitational force of the pull between the object on the earth and the earth, there is also an attraction between the two objects on the surface of the earth. The gravitational force of the moon is six times less than the gravitational force of the moon.