Question

by what factor does the gravitational force between two objects increase if the distance between them decreases by half and the masses remain the same? (1 point) 2 1 4 8

Explanation:

Step1: Recall the 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.

Step2: Analyze the change in distance

Let the original distance be \(r\), and the new distance \(r'=\frac{r}{2}\). The original force \(F = G\frac{m_1m_2}{r^2}\), and the new force \(F'=G\frac{m_1m_2}{(r')^2}\). Substitute \(r'=\frac{r}{2}\) into the new - force formula: \(F'=G\frac{m_1m_2}{(\frac{r}{2})^2}=G\frac{m_1m_2}{\frac{r^2}{4}} = 4G\frac{m_1m_2}{r^2}\)

Answer:

C. 4