Question

How does the gravitational force between two given objects change when the distance between them is reduced to one-half of its original value?

Answer 1

1. Let the masses of two given objects be M and m, and the distance between them be R.
2. Then, the magnitude of the gravitational force of attraction (F) between them is shown as $F=\frac{GMm}{R^2}$.
3. Let the value of the distance between them, after it gets halved be $\frac{R}{2}$.
4. The magnitude of the gravitational force of attraction (F') after the distance is one-halved, is given by $F\text{'}=\frac{GMm}{{\left({\displaystyle \frac{R}{2}}\right)}^2}=\frac{GMm}{{\displaystyle \frac{R^2}{4}}}=\frac{4GMm}{{\displaystyle R^2}}=4F$
5. Hence, the gravitational force between the two given objects becomes four times the original value when the distance between them is reduced to one-half of its original value.