Question

which two changes would increase the gravitational force between two objects?
a. decrease the mass of both objects.
b. increase the mass of one of the objects.
c. increase the distance between the objects.
d. decrease the distance between the objects.
e. decrease the mass of one of the objects.

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.

Step2: Analyze the effect of mass

From the formula \(F = G\frac{m_1m_2}{r^2}\), if we increase the mass of one of the objects (say \(m_1\) or \(m_2\)), the numerator \(m_1m_2\) increases. Since \(G\) and \(r\) (assuming \(r\) is constant for this analysis of mass - effect) are non - zero constants, the gravitational force \(F\) increases.

Step3: Analyze the effect of distance

From the formula \(F = G\frac{m_1m_2}{r^2}\), if we decrease the distance \(r\) between the objects, the denominator \(r^2\) decreases. Since \(G\), \(m_1\) and \(m_2\) (assuming \(m_1\) and \(m_2\) are constant for this analysis of distance - effect) are non - zero constants, the gravitational force \(F\) increases.

Answer:

B. Increase the mass of one of the objects, D. Decrease the distance between the objects.