Question

use the formula ( f = g \frac{m_1 m_2}{d^2} ), where

• ( f ) = the force of gravity
• ( g ) = universal gravitational constant
• ( m_1 ) and ( m_2 ) = masses of the two objects
• ( d ) = the distance between the centers of the two objects

what would result in the greatest gravitational force between two objects?
a halving the mass of object 1
b doubling the mass of object 1
c halving the distance between the two objects
d doubling the distance between the two objects

Explanation:

Step1: Analyze option A

If we halve the mass of object 1 (\(m_1\) becomes \(\frac{m_1}{2}\)), using the formula \(F = G\frac{m_1m_2}{d^2}\), the new force \(F_A=G\frac{\frac{m_1}{2}m_2}{d^2}=\frac{1}{2}G\frac{m_1m_2}{d^2}=\frac{F}{2}\)

Step2: Analyze option B

If we double the mass of object 1 (\(m_1\) becomes \(2m_1\)), the new force \(F_B = G\frac{2m_1m_2}{d^2}=2G\frac{m_1m_2}{d^2} = 2F\)

Step3: Analyze option C

If we halve the distance (\(d\) becomes \(\frac{d}{2}\)), the new force \(F_C=G\frac{m_1m_2}{(\frac{d}{2})^2}=G\frac{m_1m_2}{\frac{d^2}{4}} = 4G\frac{m_1m_2}{d^2}=4F\)

Step4: Analyze option D

If we double the distance (\(d\) becomes \(2d\)), the new force \(F_D=G\frac{m_1m_2}{(2d)^2}=G\frac{m_1m_2}{4d^2}=\frac{1}{4}G\frac{m_1m_2}{d^2}=\frac{F}{4}\)

Answer:

C. halving the distance between the two objects