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

3.26 kg

Explanation:

Let there b 2 bodies of mass M and m:

`\begin{gathered} F=(G\cdot M\cdot m)/(r^2) \\ \text{ In this case M = 2m, therefore:} \\ F=(G\cdot2m\cdot m)/(r^2)=(G\cdot2m^2)/(r^2) \\ F=(G\cdot2m^2)/(r^2) \\ \text{ solving for m:} \\ m^2=(r^2\cdot F)/(2\cdot G) \\ m=\sqrt[]{(r^2\cdot F)/(2\cdot G)} \\ \text{ Replacing:} \\ m=\sqrt[]{(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