Question

question 1 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 = 0.5 m
c. mass of object 1 = 15 kg
mass of object 2 = 12 kg
distance between objects = 1.5 m
d. mass of object 1 = 12 kg
mass of object 2 = 12 kg
distance between objects = 1.5 m

Explanation:

Step1: Recall the formula for gravitational force

The formula for gravitational force \(F = G\frac{m_1m_2}{r^2}\), 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: \(m_1 = 12\space kg\), \(m_2=12\space kg\), \(r = 0.5\space m\). Then \(\frac{m_1m_2}{r^2}=\frac{12\times12}{0.5^2}=\frac{144}{0.25}=576\).
• Option B: \(m_1 = 15\space kg\), \(m_2 = 12\space kg\), \(r=0.5\space m\). Then \(\frac{m_1m_2}{r^2}=\frac{15\times12}{0.5^2}=\frac{180}{0.25} = 720\).
• Option C: \(m_1 = 15\space kg\), \(m_2=12\space kg\), \(r = 1.5\space m\). Then \(\frac{m_1m_2}{r^2}=\frac{15\times12}{1.5^2}=\frac{180}{2.25}=80\).
• Option D: \(m_1 = 12\space kg\), \(m_2=12\space kg\), \(r = 1.5\space m\). Then \(\frac{m_1m_2}{r^2}=\frac{12\times12}{1.5^2}=\frac{144}{2.25}=64\).

Answer:

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