a relationship exists between gravity, mass, and distance. the greater the mass of the objects, the greater…

Explanation:

Step1: Recall gravitational - force formula

The gravitational force formula is $F = G\frac{m_1m_2}{r^2}$, 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. We can compare the cases without calculating the actual value of $F$ by looking at the product $\frac{m_1m_2}{r^2}$.

Step2: Calculate $\frac{m_1m_2}{r^2}$ for each option

Option 1:

$m_1 = m_2=10\ kg$, $r = 10\ m$. Then $\frac{m_1m_2}{r^2}=\frac{10\times10}{10^2}=\frac{100}{100} = 1$.

Option 2:

$m_1 = m_2 = 20\ kg$, $r = 10\ m$. Then $\frac{m_1m_2}{r^2}=\frac{20\times20}{10^2}=\frac{400}{100}=4$.

Option 3:

$m_1 = m_2 = 20\ kg$, $r = 15\ m$. Then $\frac{m_1m_2}{r^2}=\frac{20\times20}{15^2}=\frac{400}{225}\approx1.78$.

Option 4:

$m_1 = m_2 = 10\ kg$, $r = 15\ m$. Then $\frac{m_1m_2}{r^2}=\frac{10\times10}{15^2}=\frac{100}{225}\approx0.44$.

Step3: Compare the results

We can see that the value of $\frac{m_1m_2}{r^2}$ is the largest for Option 2.

Answer:

two objects, each with a mass of 20 kg, separated by a distance of 10 m