Question

7 multiple choice 1 point we know that gravitational force goes down with distance. if distance is cut in half, by how much does the force change? (for this problem, you can assume $gm_1m_2 = 1$.) 4 times more 1/2 2 times more 1/4

Explanation:

Step1: Recall Gravitational Force Formula

The gravitational force formula is \( F = G\frac{m_1m_2}{r^2} \), where \( F \) is the force, \( G \) is the gravitational constant, \( m_1, m_2 \) are masses, and \( r \) is the distance between them. Given \( Gm_1m_2 = 1 \), so \( F=\frac{1}{r^2} \).

Step2: Analyze Distance Change

Original distance: \( r \), new distance: \( r'=\frac{r}{2} \).

Step3: Calculate New Force

Substitute \( r' \) into the force formula: \( F'=\frac{1}{(r')^2}=\frac{1}{(\frac{r}{2})^2}=\frac{1}{\frac{r^2}{4}}=\frac{4}{r^2} \).
Original force \( F = \frac{1}{r^2} \), so \( F' = 4F \), meaning the force becomes 4 times more.

Answer:

A. 4 times more