Question

The mass of the earth is $6\times {{10}^{24}}kg$ and that of the moon is $7.4\times {{10}^{22}}kg$ . Let the distance between the moon and the earth is found to be $3.84\times {{10}^{5}}km$. Then what will be the force exerted by the earth on the moon. Let us take gravitational constant as $G=6.7\times {{10}^{-11}}N{{m}^{2}}k{{g}^{-2}}$.

Answer 1

Hint: the gravitational force acting on a body can be found by taking the ratio of the product of the gravitational constant, mass of the earth and mass of the body to the square of the distance between them. Substitute all these values mentioned in the question in this equation. This will help you in answering this question.

Complete step by step answer:
 the gravitational force acting on a body can be found by taking the ratio of the product of the gravitational constant, mass of the earth and mass of the body to the square of the distance between them. Therefore we can write that,
$F=\dfrac{G{{M}_{e}}{{M}_{m}}}{{{R}^{2}}}$
Where $G$be the gravitational constant which is having the value given as,
$G=6.7\times {{10}^{-11}}N{{m}^{2}}k{{g}^{-2}}$
${{M}_{e}}$ be the mass of the earth which has been mentioned to be as,
${{M}_{e}}=6\times {{10}^{24}}kg$
Mass of the moon has been given as,
${{M}_{m}}=7.4\times {{10}^{22}}kg$
The distance between the moon and the earth has been mentioned to be as,
$R=3.84\times {{10}^{5}}km=3.84\times {{10}^{8}}m$
This values can be substituted in the equation now as,
\[F=\dfrac{6.7\times {{10}^{-11}}\times 6\times {{10}^{24}}\times 7.4\times {{10}^{22}}}{{{\left( 3.84\times {{10}^{8}} \right)}^{2}}}\]
Simplifying this equation can be shown as,
\[F=\dfrac{297.48\times {{10}^{-11+24+22}}}{{{\left( 3.84 \right)}^{2}}\times {{10}^{16}}}=20.17\times {{10}^{19}}=2.017\times {{10}^{20}}N\]
Hence the force has been found to be as \[2.017\times {{10}^{20}}N\]. Therefore the answer for the question has been obtained.

Note: Gravity or otherwise called as gravitation is basically a natural phenomenon by which all matters with mass or energy consisting of planets, stars, galaxies, and also light are taken towards one another. On the earth, gravity is giving weight to physical bodies. The gravity of the moon is resulting in the ocean tides.