Question

Two objects are placed so their centers are 1.21 meters apart, and the force between them is 9.71 x 10^-10 newtons. What is the mass of each object if one has twice the mass of the other? Include units in your answers. Answer must be in 3 significant digits.

Answer 1

ANSWER:

3.26 kg

STEP-BY-STEP EXPLANATION:

Let there b 2 bodies of mass M and m:

$\begin{gathered} F=\frac{G\cdot M\cdot m}{r^2} \\ \text{ In this case M = 2m, therefore:} \\ F=\frac{G\cdot2m\cdot m}{r^2}=\frac{G\cdot2m^2}{r^2} \\ F=\frac{G\cdot2m^2}{r^2} \\ \text{ solving for m:} \\ m^2=\frac{r^2\cdot F}{2\cdot G} \\ m=\sqrt[]{\frac{r^2\cdot F}{2\cdot G}} \\ \text{ Replacing:} \\ m=\sqrt[]{\frac{1.21^2\cdot9.71\cdot10^{-10}}{2\cdot6.67259\cdot10^{-11}}} \\ m=3.26\text{ kg} \end{gathered}$

The mass is 3.26 kg