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hichkok12 [17]
2 years ago
12

If the distance between the Earth and Moon were half what it is now, by what factor would the force of gravity between them be c

hanged. That is, what is the ratio of the new force to the old force?
Physics
1 answer:
hichkok12 [17]2 years ago
7 0

Answer:

4

Explanation:

G = Gravitational constant = 6.67 × 10⁻¹¹ m³/kgs²

m_1 = Mass of Earth

m_2 = Mass of Moon

r = Distance between Earth and Moon

Old gravitational force

F_o=\dfrac{Gm_1m_2}{r^2}

New gravitational force

F_n=\dfrac{Gm_1m_2}{(\dfrac{1}{2}r)^2}

Dividing the equations

\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

The ratio is \dfrac{F_n}{F_o}=4

The new force would be 4 times the old force

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