Question

in the simulation, change the mass of the two objects and observe the gravitational force. what happens to the gravitational force when the mass of both objects is tripled? a) the gravitational force increases by a factor of 3. b) the gravitational force increases by a factor of 9. c) the gravitational force increases by a factor of 6. d) the gravitational force decreases by a factor of 3.

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 tripling both masses

If \( m_1' = 3m_1 \) and \( m_2' = 3m_2 \), then the new force \( F' = G\frac{(3m_1)(3m_2)}{r^2}=9G\frac{m_1m_2}{r^2} \).

Answer:

B. The gravitational force increases by a factor of 9.