Question

What happens to the force between two objects, if

(i) the mass of one object is doubled?
(ii) the distance between the objects is doubled and tripled?
(iii) the masses of both objects are doubled?

Answer 1

According to the universal law of gravitation, gravitational force acting between two objects of mass M and m separated by distance r is given by
\(F=G \frac{M \times m}{r^2}\)

(i) When mass of one of the objects, say m, is doubled then
\(F^{'}=G \frac{M \times 2m}{r^2}=2F\)
So when the mass of any one of the objects is doubled, the force is also doubled.

(ii) The force F is inversely proportional to the square of the distance between the objects. So if the distance between two objects is doubled then the gravitational force of attraction between them is reduced to one-fourth of the original value.
\(F^{'}=G \frac{M \times m}{(2r)^2}=F/4\)

Similarly, if the distance between two objects is tripled, then the gravitational force of attraction becomes one-ninth the original value.
\(F^{'}=G \frac{M \times m}{(3r)^2}=F/9\)

(iii) The gravitational force F is directly proportional to the product of the masses. So if both the masses are doubled then the gravitational force of attraction becomes four times the original value.
\(F^{'}=G \frac{2M \times 2m}{r^2}=4F\)