Question

According to Newton’s Law of Universal Gravitation, how would the gravitational force between the Earth and the moon change if the moon were twice as massive as it is today?

Answer 1

The new force becomes twice of the initial force.

Step-by-step explanation:

The Newton’s Law of Universal Gravitation between the Earth and the moon is given by :

`F=G(m_em_m)/(r^2)`

Here,

`m_e\ and\ m_e` are mass of Earth and the Moon

r is the distance between Moon and Earth

According to given condition, if the moon were twice as massive as it is today,
`m'_m=2m_m`

New force becomes,

`F'=G(m_em'_m)/(r^2)`

`F'=G(m_e(2m_m))/(r^2)`

`F'=2* G(m_em_m)/(r^2)`

`F'=2F`

So, the new force becomes twice of the initial force. Hence, this is the required solution.