Question

What is the magnitude of the gravitational force between the earth and a $1\mathrm{kg}$ object on its surface? (Mass of the earth is $6\times {10}^{24}\mathrm{kg}$m and radius of the earth is $6.4\times {10}^6\mathrm{m}$.)

Answer 1

Step 1: Given information

Mass of object, ${\mathrm{m}}_1=1\mathrm{kg}$.

Mass of earth, ${\mathrm{m}}_2=6\times {10}^{24}\mathrm{kg}$

Radius of earth, $\mathrm{R}=6.4\times {10}^6\mathrm{m}$

Step 2: Write an expression for the magnitude of gravitational force as follows:

$F=\frac{G{m}_1{m}_2}{R^2}$

Here, $G$ is the gravitational constant.

Substitute $1\text{kg}$ for ${\mathrm{m}}_1$, $6\times {10}^{24}\text{kg}$ for ${\mathrm{m}}_2$, $6.4\times {10}^6\mathrm{m}$ for $\mathrm{R}$ and $6.67\times {10}^{-11}\frac{{\text{Nm}}^2}{{\text{kg}}^2}$ for $\mathrm{G}$ in expression of gravitational force

$\mathrm{F}=\frac{\left(6.67\times {10}^{-11}{\displaystyle \frac{{\mathrm{Nm}}^2}{{\mathrm{kg}}^2}}\right)\times 1\mathrm{kg}\times 6\times {10}^{24}\mathrm{kg}}{{\left(6.4\times {10}^6\mathrm{m}\right)}^2}=9.8\mathrm{N}$

Hence, magnitude of the gravitational force is $9.8\mathrm{N}$.