Question

in the simulation, adjust the distance and observe the effect on the gravitational force. how does the gravitational force change if the distance between two objects is doubled? a) the gravitational force doubles. b) the gravitational force decreases by a factor of 4. c) the gravitational force increases by a factor of 4. d) the gravitational force remains unchanged.

Explanation:

Step1: Recall the formula for gravitational force

The formula for gravitational force between two objects is \( F = \frac{Gm_1m_2}{r^2} \), 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 doubling the distance

If the distance \( r \) is doubled (\( r' = 2r \)), then the new force \( F'=\frac{Gm_1m_2}{(2r)^2}=\frac{Gm_1m_2}{4r^2} \).

Step3: Compare the new force with the original force

We can see that \( F'=\frac{1}{4}F \), which means the gravitational force decreases by a factor of 4.

Answer:

B) The gravitational force decreases by a factor of 4.