Question

What is the value of acceleration due to gravity of the Earth?
(Given mass of the Earth is $6\times {10}^{24}kg$ and radius of the Earth is $6.4\times$ ${10}^{6}m$).

• A. $9.8cm{s}^{-2}$
• B. $9.8m{s}^{-2}$
• C. $9.8km{s}^{-2}$
• D. $9.8mm{s}^{-2}$

Answer 1

The correct option is B $9.8m{s}^{-2}$

According to universal law of gravitation, gravitational force is given by:
$F=\frac{GmM}{R^2}$​
For objects close to earth, $R$ is the radius of earth.

This causes acceleration in a body called the acceleration due to gravity. Using Newton's second law,
$F=mg$

$⟹mg=\frac{GMm}{R^2}$
$g=\frac{GM}{R^2}$
Substituting values of these constants, we get:
$g=\frac{6.67\times {10}^{-11}\times 6\times {10}^{24}}{{(6.4\times {10}^6)}^2}$​
$g\approx 9.8m{s}^{-2}$