Answer to Question #220916 in Classical Mechanics for DUMANNY

Question

Question 2 options:

Given the value for the universal gravitational constant, the average value for the acceleration due to gravity at the surface of Earth, and the radius of Earth, Earth’s mass is ____x10²⁴kg

Answer 1

We have, acceleration due to gravity,

$g = \frac {GM} {R2}$

Where, G = Gravitational constant

= $6.67×10^{-11} N.m^2/kg^2,$

R = radius of the Earth = $6.4×10^6 m$ ,

g = acceleration due to gravity on Earth surface

= 9.8 m/s2 and M is the mass of Earth, then, we can write,

$9.8 = 6.67×10^{-11} ×\frac {M} {(6.4×10^6)^2}$

=> $9.8 = M×0.16284×10^{-23}$

So, mass of Earth = $\frac {9.8} {(0.16284×10^{-23} ) kg}$

= $5.97×10^{24} kg$