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.

Respuesta :

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

[tex]F=8.16\times10^{-10}\text{ N}[/tex]

The formula for the force can be written as

[tex]F=\frac{Gm\times2m}{r^2}[/tex]

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

The mass will be

[tex]m^{}=\sqrt{\frac{Fr^2}{2G}}[/tex]

Substituting the values, the mass will be

[tex]\begin{gathered} m=\sqrt[]{\frac{8.16\times10^{-10}\times(1.19)^2}{2\times6.67\times10^{-11}}} \\ =\sqrt[]{8.662} \\ =2.943\text{ kg} \end{gathered}[/tex]

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

[tex]\begin{gathered} 2\times2.943 \\ =\text{ 5.886 kg} \end{gathered}[/tex]