Question

the information in the table represents the effect of the mass of two objects on the gravitational force between the two objects.

mass of object 1 (kg)	mass of object 2 (kg)	distance between objects 1 and 2 (m)	gravitational force between objects 1 and 2 (n)
2	1	1	?

which number should be in the cell with the question mark?
the number is two because when you double the mass of one of the objects, the force between the objects is halved.
the number is four because when you double the mass of one of the objects, the force between the objects remains the same.
the number is eight because when you double the mass of one of the objects, the force between the objects also doubles.
the number is sixteen because when you double the mass of one of the objects, the force between the

Explanation:

Step1: Recall gravitational - force formula

The gravitational force formula is $F = G\frac{m_1m_2}{r^2}$, where $F$ is the gravitational force, $G$ is the gravitational constant, $m_1$ and $m_2$ are the masses of the two objects, and $r$ is the distance between them. When $r$ is constant, $F\propto m_1m_2$.

Step2: Analyze the change in mass

In the first row, $m_1 = 1$, $m_2 = 1$, and $F = 4$. In the second row, $m_1$ is doubled to 2, $m_2=1$, and $r$ remains 1. Since $F\propto m_1m_2$ and $r$ is constant, when $m_1$ doubles from 1 to 2 and $m_2$ and $r$ are unchanged, the new force $F_{new}$ is related to the old force $F_{old}$ by $\frac{F_{new}}{F_{old}}=\frac{m_{1 - new}m_{2 - new}}{m_{1 - old}m_{2 - old}}$. Substituting the values, we have $\frac{F_{new}}{4}=\frac{2\times1}{1\times1}=2$. So $F_{new}=8$.

Answer:

The number is eight because when you double the mass of one of the objects, the force between the objects also doubles. So the correct option is: The number is eight because when you double the mass of one of the objects, the force between the objects also doubles.