Physics GRE - #31

Which of the following is nearly the mass of the Earth? The radius of the Earth is about $6.4\cdot10^6\,\text{m}$.

1. $6\cdot10^{24}\,\text{kg}$
2. $6\cdot10^{27}\,\text{kg}$
3. $6\cdot10^{30}\,\text{kg}$
4. $6\cdot10^{33}\,\text{kg}$
5. $6\cdot10^{36}\,\text{kg}$

Solution :

Choice 1 is the answer.

If you don't remember the mass of the earth off the bat, recall that at ground level, \[mg=\frac{GmM_E}{R_E^2}\implies M=\frac{gR_E^2}{G}\] where $g$, $G$, and $R_E$ are given constants (a table of constants is given during the exam). We can plug in the numbers and compute \[M_E\approx6\cdot10^{24}\,\text{kg}.\]