### Video Transcript

If the gravitational force between two masses was 10 newtons at a certain distance, what would the gravitational force become if that distance was doubled?

Newtonβs law of universal gravitation states that for two masses π one and π two, the force of gravity πΉ between them will be given by the following relation: πΉ is equal to πΊ multiplied by π one multiplied by π two divided by π squared, where πΊ is the gravitational constant, π one and π two are the two masses, and π is the distance between them.

In this case, we have that 10 is equal to πΊ multiplied by π one multiplied by π two divided by π squared. Our new force πΉ one when the distance has doubled is equal to πΊ multiplied by π one multiplied by π two divided by two π squared. As two π all squared is equal to four π squared, we can say that πΉ one is equal to πΊ multiplied by π one multiplied by π two divided by four π squared.

This can be rewritten as πΉ one is equal to a quarter of πΊ multiplied by π one multiplied by π two divided by π squared. As the initial gravitational force was equal to 10 newtons, we can substitute 10 into this equation: πΊ multiplied by π one multiplied by π two divided by π squared is equal to 10.

This means that πΉ one is equal to a quarter multiplied by 10. A quarter of 10 is five over two or five halves. This is equal to 2.5 newtons. Therefore, when the distance between the two masses is doubled, the gravitational force has quartered or we have divided it by four.