Answer: [tex]M = 5.98\times 10^{24} kg[/tex]
Explanation:
We know that force acting on an object due to Earth's gravity on the surface is given by:
[tex]mg = G\frac{Mm}{r^2}\\ \Rightarrow g = \frac{GM}{r^2}[/tex]
where g is the acceleration due to gravity, r would be radius of Earth, M is the mass of Earth and G is the gravitational constant.
It is given that at pole, g = 9.830 m/s² and r = 6371 km = 6371 × 10³ m
[tex]\Rightarrow M = \frac{g\times r^2}{G}[/tex]
[tex]M = \frac{9.830 m/s^2 \times (6371 \times 10^3 m )^2}{6.67 \times 10^{-11} m^3 kg^{-1} s^{-2}}[/tex]
[tex]\Rightarrow M = 5.98\times 10^{24} kg[/tex]
Hence, Earth's mass is [tex] 5.98\times 10^{24} kg[/tex]
