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

Answer:

$8000\ N$

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 $(d)$.

$F_g=\frac{K}{d^2}$

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,

$2000=\frac{K}{100^2}\\ So,\ K=2000\times 100^2$

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

$F'_g=\frac{K}{50^2} \\\\F'_g=\frac{2000\times 100^2}{50^2}\\ \\F'_g=2000\times 4=8000\ N$

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