Question

Two objects are placed so their centers are 1.54 meters apart, and the force between them is 7.14 x 10-10 newtons. What is the mass of each object if one has twice the mass of the other?

Answer 1

Given:

The distance between the two objects is r = 1.54 m

The force between the two objects is

$F=\text{ 7.14}\times10^{-10}\text{ N}$

Let the mass of the object is m and the mass of the other object is 2m

To find the mass of each object.

Explanation:

The mass can be calculated by the formula

$\begin{gathered} F=\frac{Gm\times(2m)}{r^2} \\ m=\frac{Fr^2}{2G} \end{gathered}$

Here, G is the universal gravitational constant whose value is

$G\text{ = 6.67}\times10^{-11}\text{ N m}^2\text{ /kg}^2$

On substituting the values, the mass will be

$\begin{gathered} m=\frac{7.14\times10^{-10}\times(1.54)^2}{2\times6.67\times10^{-11}} \\ =12.69\text{ kg} \end{gathered}$

The mass of the other object will be

$2m\text{ = 25.38 kg}$

Final Answer:

The mass of the first object is 12.69 kg

The mass of the second object is 25.38 kg