Question

The mass of two bodies is doubled and the distance is halved, how will the gravitational force change?

Answer 1

STEP 1

The gravitational force between two objects is given by

$$\begin{gathered} {\text{F=GMm/r}}^2 \\ \text{Where,} \\ \text{G=Gravitational constant} \\ \text{M=Mass of object1} \\ \text{m=Mass of object 2} \\ \text{r=Distance between the two object.} \end{gathered}$$

STEP 2 Given:

$$\begin{gathered} \text{Mass of object 1= 2M} \\ \text{Mass of object 2= 2m} \\ \text{Distance between them=r/2} \\ \text{F=G}\left(\text{2M}\right)\left(\text{2m}\right)/{\left(\text{r/2}\right)}^2 \\ F{\text{=4GMm/r}}^2\text{/4} \\ F=16\left({\text{GMm/r}}^2\right) \end{gathered}$$

Hence, the new gravitational force will be sixteen times the initial force.