Question

The radius of earth is 6400 km. What is its mass?

• A. $6.0\times {10}^{24}$kg
• B. $5.0\times {10}^{24}$kg
• C. $1.0\times {10}^{22}$kg
• D. $6.5\times {10}^{14}$kg

Answer 1

The correct option is A

$6.0\times {10}^{24}$kg

Step1:

Given data:

The radius of the earth $r=6400km$

Acceleration of due to gravity $g=0.0098\raisebox{1ex}{$km$}\!\left/ \!\raisebox{-1ex}{$s^2$}\right.$

Gravitational constant $G=6.67\times {10}^{-20}k{g}^{-1}k{m}^{-3}{s}^{-2}$

Step2: Calculate the mass of the earth

$$\begin{gathered} \Rightarrow m=r^2\times \frac{g}{G} \\ \Rightarrow m={\left(6400\right)}^2\times \frac{0.0098}{6.67\times {10}^{-20}} \\ \Rightarrow m=\frac{401408}{6.67\times {10}^{-20}} \\ \Rightarrow m=60181.1094\times {10}^{20} \\ \Rightarrow m=6.0\times {10}^{24}kg \end{gathered}$$

Hence, we conclude that option (A) is the correct answer