Question

What is the gravitational force fg between the two objects described in part b if the distance between them is only 50 km ?

Answer 1

`8000\ N`

Step-by-step explanation:

The question is incomplete.

The complete question would be

B) Suppose the magnitude of the gravitational force between two spherical objects is 2000 N when they are 100 km apart. What is the gravitational force
`F_g` between the two objects described in Part B if the distance between them is only 50 km.

Given gravitational force between two object
`F_g=2000\ N` when objects are placed
`100\ km` apart.

We need to determine gravitational force when they are kept
`50\ km` apart.

As we know the gravitational force
`F_g` is inversely proportional to the square of distance between objects
`(d)`.

`F_g=(K)/(d^2)`

Where
`K=Gm_1m_2` that will be constant. Because the mass of the object remain same in both cases. And
`G` is already gravitational constant.

Given,

`2000=(K)/(100^2)\\ So,\ K=2000* 100^2`

Let
`F'_g` is the force between objects when they were kept
`50\ km` apart.

`F'_g=(K)/(50^2) \\\\F'_g=(2000* 100^2)/(50^2)\\ \\F'_g=2000* 4=8000\ N`

So,
`8000\ N` is the gravitational force when two objects were kept
`50\ km` apart.