Question

3.3.2 test (cst): forces
question 9 of 20
in which scenario will the two objects have the greatest gravitational force between them?
a. mass of object 1 = 12 kg
mass of object 2 = 12 kg
distance between objects = 0.5 m
b. mass of object 1 = 15 kg
mass of object 2 = 12 kg
distance between objects = 1.5 m
c. mass of object 1 = 12 kg
mass of object 2 = 12 kg
distance between objects = 1.5 m
d. mass of object 1 = 15 kg
mass of object 2 = 12 kg
distance between objects = 0.5 m

Explanation:

Step1: Recall the formula for gravitational force

The formula for gravitational force 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. Since \(G\) is a constant, we can compare the values of \(\frac{m_1m_2}{r^2}\) for each option.

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

• Option A:

\(\frac{m_1m_2}{r^2}=\frac{12\times12}{0.5^2}=\frac{144}{0.25} = 576\)

• Option B:

\(\frac{m_1m_2}{r^2}=\frac{15\times12}{1.5^2}=\frac{180}{2.25}=80\)

• Option C:

\(\frac{m_1m_2}{r^2}=\frac{12\times12}{1.5^2}=\frac{144}{2.25} = 64\)

• Option D:

\(\frac{m_1m_2}{r^2}=\frac{15\times12}{0.5^2}=\frac{180}{0.25}=720\)

Answer:

D. Mass of object 1 = 15 kg, Mass of object 2 = 12 kg, Distance between objects = 0.5 m