Question

What happens to the forces between two objects, if :
The masses of both objects are doubled?

Answer 1

Step 1: Gravitational force formula,

As we know that gravitational force between two objects is given by

$\mathrm{F}=\frac{\mathrm{GMm}}{{\mathrm{r}}^2}$

Where G = Gravitational force

M = Mass of object 1

m = Mass of object 2

r = Distance between the two objects

Step 2: When the masses of both objects are doubled

New Mass of Object 1 = 2M

New Mass of Object 2 = 2m

Thus,

New force = $\frac{\mathrm{G}\times 2\mathrm{M}\times 2\mathrm{m}}{{\mathrm{r}}^2}$

= $\frac{4\mathrm{GMm}}{{\mathrm{r}}^2}$

= $4\times$initial force

⸫ If the mass of both objects is doubled, the force becomes four times