Question

How does the gravitational force between two objects change if the distance between the objects is cut in half?

Answer 1

D. the gravitational force increases by a factor of 4

Explanation:

The magnitude of the gravitational force between two objects is given by:

$F=G\frac{m_1 m_2}{r^2}$

where

$G=6.67\cdot 10^{-11} m^3 kg^{-1}s^{-2}$ is the gravitational constant

m1, m2 are the masses of the two objects

r is the separation between them

Here let's call F the initial gravitational force between the two objects. Later, the distance between the objects is halved, so the new distance is:

$r'=\frac{r}{2}$

Substituting into the equation, we find the new force:

$F'=G\frac{m_1 m_2}{(r/2)^2}=4(G\frac{m_1 m_2}{r^2})=4F$

Therefore, the gravitational force increases by a factor of 4.

Learn more about gravitational force:

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