Question

an increase in distance between two objects will ____ the gravitational force between them. an increase in the total mass of two objects will ____ the gravitational force between them.
a. decrease; decrease
b. decrease; increase
c. increase; increase
d. increase; decrease

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.

Step2: Analyze the effect of distance

When the distance \(r\) increases, since \(F\) is inversely proportional to \(r^2\) (\(F\propto\frac{1}{r^2}\)), the gravitational force \(F\) will decrease.

Step3: Analyze the effect of mass

When the total mass (\(m_1 + m_2\)) increases (assuming at least one of \(m_1\) or \(m_2\) increases), since \(F\) is directly proportional to \(m_1m_2\) (\(F\propto m_1m_2\)), the gravitational force \(F\) will increase.

Answer:

B. decrease; increase