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

the information in the table represents the effect of the mass of two objects on the gravitational force between the two objects.\n|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)|\n|----|----|----|----|\n|1|1|1|4|\n|2|1|1|?|\nwhich number should be in the cell with the question mark?\nthe number is two because when you double the mass of one of the objects, the force between the objects is halved.\nthe number is four because when you double the mass of one of the objects, the force between the objects remains the same.\nthe number is eight because when you double the mass of one of the objects, the force between the objects also doubles.\nthe number is sixteen because when you double the mass of one of the objects, the force between the objects increases by a factor of 4.
Answer
Answer:
The number is eight because when you double the mass of one of the objects, the force between the objects also doubles.
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.
Step2: Analyze the first row
In the first row, $m_1 = 1$ kg, $m_2 = 1$ kg, $r = 1$ m, and $F = 4$ N. So, $4=G\frac{1\times1}{1^2}=G$.
Step3: Analyze the second row
In the second row, $m_1 = 2$ kg, $m_2 = 1$ kg, $r = 1$ m. Using $F = G\frac{m_1m_2}{r^2}$ and since $G = 4$ (from Step 2), we have $F=4\times\frac{2\times1}{1^2}=8$ N. So when we double the mass of one of the objects (from 1 kg to 2 kg while keeping other factors the same), the force doubles from 4 N to 8 N.