Question

Two objects are placed so their centers are 1.19 meters apart, and the force between them is 8.16 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. Answers must be in 3 significant digits.

Answer 1

Given that the mass of object 1 is m and the mass of object 2 is 2m.

The distance between two objects is r = 1.19 m

The force between two objects is

`F=8.16*10^(-10)\text{ N}`

The formula for the force can be written as

`F=(Gm*2m)/(r^2)`

Here, the universal gravitational constant is G = 6.67 x 10^(-11) m^3 kg^(-1)s^(-2)

The mass will be

`m^{}=\sqrt{(Fr^2)/(2G)}`

Substituting the values, the mass will be

`\begin{gathered} m=\sqrt[]{(8.16*10^(-10)*(1.19)^2)/(2*6.67*10^(-11))} \\ =\sqrt[]{8.662} \\ =2.943\text{ kg} \end{gathered}`

The mass of object 1 is 2.94 kg and the mass of object 2 is

`\begin{gathered} 2*2.943 \\ =\text{ 5.886 kg} \end{gathered}`