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

Explanation:

Step1: Recall gravitational - force formula

The gravitational force between two objects is given by $F = G\frac{m_1m_2}{r^2}$, where $G$ is the gravitational constant, $m_1$ and $m_2$ are the masses of the two objects, and $r$ is the distance between them. In this case, $r$ is constant ($r = 1m$), and $G$ is a constant. Let the initial masses be $m_{11}=1kg$ and $m_{21}=1kg$, and the initial force $F_1 = 4N$. So, $F_1=G\frac{m_{11}m_{21}}{r^2}=4N$.

Step2: Analyze the new - mass situation

The new mass of object 1 is $m_{12}=2kg$, and $m_{22}=1kg$, and $r = 1m$. The new force $F_2=G\frac{m_{12}m_{22}}{r^2}$. Since $m_{12} = 2m_{11}$ and $m_{22}=m_{21}$ and $r$ is the same, we have $F_2=G\frac{2m_{11}m_{21}}{r^2}=2\times G\frac{m_{11}m_{21}}{r^2}$.

Step3: Calculate the new force

Since $G\frac{m_{11}m_{21}}{r^2}=F_1 = 4N$, then $F_2 = 2F_1$. Substituting $F_1 = 4N$, we get $F_2=8N$.

Answer:

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