Question

The mass of Earth is $6\times {10}^{24}kg$ and radius of Earth is $6.4\times {10}^{6}m$and $G=6.7\times {10}^{-11}N{m}^2/k{g}^2$.The acceleration due to gravity on the surface of earth is:

• A. $9.70m{s}^{-2}$
• B. $9.78m{s}^{-2}$
• C. $9.89m{s}^{-2}$
• D. $9.80m{s}^{-2}$

Answer 1

The correct option is D

$9.80m{s}^{-2}$

Step 1: Given data

Mass of Earth, $M=6\times {10}^{24}kg$

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

Acceleration due to gravity, $g=?$ (To be calculated)

Step 2: Calculating acceleration due to gravity

Applying, $g=\frac{G\times M}{R^2}$

$$\begin{gathered} \Rightarrow g=\frac{6.67\times {10}^{-11}N{m}^2/k{g}^2\times 6\times {10}^{24}kg}{{(6.4\times {10}^{6}m)}^2} \\ \Rightarrow g=9.80m{s}^{-2} \end{gathered}$$

Hence, the correct answer is option (D) i.e. $9.80m{s}^{-2}$