Question

Two objects are placed so their centers are 1.35 meters apart, and the force between them is 6.19 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

The distance between the two masses is d = 1.35 m

The force between the masses is

$F=6.19\times10^{-10}\text{ N}$

Let the mass of object 1 be m.

Let the mass of object 2 be 2m.

The formula of force can be written as

$F=\frac{Gm\times2m}{d^2}$

Here, the universal gravitational constant is

$G=6.67\text{ }\times\frac{10^{-11}Nm^2}{\operatorname{kg}}$

The mass can be calculated as

$\begin{gathered} m=\frac{Fd^2}{2G} \\ =\frac{6.19\times10^{-10}\times(1.35)^2}{2\times6.67\times10^{-11}} \\ =8.45\text{ kg} \end{gathered}$

The mass of object 2 is

$2m=16.9\text{ kg}$

The mass of the first object is 8.45 kg.

The mass of the second object is 16.9 kg.