Question

What happens to the forces between two objects, if :
The mass of the one object is doubled?

Answer 1

Step 1: Gravitatioanl force,

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 mass of one object is doubled

Let Mass of Object 1 be doubled

New Mass of Object 1= 2 M

Thus,

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

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

= $2\times$initial value

Thus, if the mass of one object is doubled, then the force is also doubled.