Answer:
4
Explanation:
G = Gravitational constant = 6.67 × 10⁻¹¹ m³/kgs²
[tex]m_1[/tex] = Mass of Earth
[tex]m_2[/tex] = Mass of Moon
r = Distance between Earth and Moon
Old gravitational force
[tex]F_o=\dfrac{Gm_1m_2}{r^2}[/tex]
New gravitational force
[tex]F_n=\dfrac{Gm_1m_2}{(\dfrac{1}{2}r)^2}[/tex]
Dividing the equations
[tex]\dfrac{F_n}{F_o}=\dfrac{\dfrac{Gm_1m_2}{(\dfrac{1}{2}r)^2}}{\dfrac{Gm_1m_2}{r^2}}\\\Rightarrow \dfrac{F_n}{F_o}=\dfrac{\dfrac{Gm_1m_2}{\dfrac{1}{4}r^2}}{\dfrac{Gm_1m_2}{r^2}}\\\Rightarrow \dfrac{F_n}{F_o}=4[/tex]
The ratio is [tex]\dfrac{F_n}{F_o}=4[/tex]
The new force would be 4 times the old force
