Question

What is the value of acceleration due to the gravity of the Earth?

• A. 9.8 m/s²
• B. 9.8 cm/s²
• C. 9.8 mm/s²
• D. All of these

Answer 1

The correct option is A

9.8 m/s²

Magnitude of the gravitational force F will be equal to the product of mass and acceleration due to the gravitational force, i.e., F = mg
Force of gravitation = [($\frac{Gm{M}_{earth}}{r^2}$)​] = mg,
Where, m = mass of object and M = mass of the Earth, r = radius of the Earth (separation between object and Earth)
Thus after cancellation of m from both the sides, we get, g = $\frac{G{M}_{earth}}{r^2}$​
G = 6.67 $\times$ ${10}^{-11}$​, Mass of the Earth = 6 $\times$ ${10}^{24}$​​ kg and r = 6.4 $\times$ ${10}^6$​​ m
$g=\frac{6.67\times {10}^{-11}\times 6\times {10}^{24}}{{(6.4\times {10}^6)}^2}$​
$g=9.8\frac{m}{s^2}$