Question

Two objects are placed so their centers are 1.65 meters apart, and the force between them is 8.09 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

Given that the distance between two objects is r = 1.65 m

The force between the objects is

$F=8.09\times10^{-10}\text{ N}$

If the mass of object 1 is m then the mass of object 2 will be 2m

The gravitational force will be

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

Here, G is the universal gravitational constant whose value is

$G=6.6\times10^{-11}Nm^2kg^{-2}$

The mass can be calculated as

$m^{}=\sqrt{\frac{Fr^2}{2G}}$

Substituting the values, the mass will be

$m=16.685\text{ kg}$

The mass of object 2 will be

$2m=33.37\text{ kg}$