Question

What is the gravitational force on body of mass $150Kg$ lying on the surface of earth.

Mass of earth given is $6\times {10}^{24}Kg$. radius of earth is $6.4\times {10}^{6}m$.

Answer 1

Step 1: Given data:

Mass of earth=$m_e=6\times {10}^{24}Kg$

Mass of the body =$m_b=150Kg$

The radial distance between body and earth =$r=6.4\times {10}^{6}m$

Step 2: Finding force

The value of the gravitational constant is specified and is given as

$G=6.7\times {10}^{-11}N{m}^{2}K{g}^2$

According to the universal law of gravitation, “Each body attracts every other body with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them"

Mathematically it is represented as

$$\begin{gathered} F=\frac{G{m}_1{m}_2}{r^2}N \\ \text{Substituting the values into the formula} \\ F=\left(\frac{6.7\times {10}^{-11}\times 150\times 6\times {10}^{24}}{{\left(6.4\times {10}^6\right)}^2}\right)N \\ =1472N \end{gathered}$$

Thus, the $1427N$ is the gravitational force on the body.

Hence, the calculated value of the force of gravitation by the body on the surface of the earth is given as $1472N$.