Question

The magnitude of the force of gravity between two identical objects is given to be F0. Calculate the new force of gravity between the objects if the mass of each object and the distance between them is doubled.

Answer 1

The force of gravity between two objects is given by:

$F=G\frac{m_1m_2}{r^2}$

where G is the gravitational constant, m1 and m2 are the masses of the objects and r is the distance between them.

In this case we know that the objects are identical, this means that the masses are the same:

$\begin{gathered} m_1=m_2 \\ \text{for simplicity let's call them }m \end{gathered}$

Then we have that:

$F_0=G\frac{m^2}{r^2}$

Now, if we double the mass of each object and the distance between them we have that:

$\begin{gathered} F=G\frac{(2m)^2}{(2r)^2} \\ F=G\frac{4m^2}{4r^2} \\ F=G\frac{m^2}{r^2} \\ F=F_0_{} \end{gathered}$

Therefore the new force is the same if doubled both the mass of each object and the distance between them.