Question

Calculate earth's mass given the acceleration due to gravity at the north pole is 9.830 m/s2 and the mean radius of the earth at the north pole is 6371 km.

Answer 1

Answer: $M = 5.98\times 10^{24} kg$

Explanation:

We know that force acting on an object due to Earth's gravity on the surface is given by:

$mg = G\frac{Mm}{r^2}\\ \Rightarrow g = \frac{GM}{r^2}$

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

$\Rightarrow M = \frac{g\times r^2}{G}$

$M = \frac{9.830 m/s^2 \times (6371 \times 10^3 m )^2}{6.67 \times 10^{-11} m^3 kg^{-1} s^{-2}}$

$\Rightarrow M = 5.98\times 10^{24} kg$

Hence, Earth's mass is $5.98\times 10^{24} kg$