Respuesta :
Increase of distance by a factor of 3 decreases the gravitational force by a factor of 9 and increase of distance by a factor of 4 decreases the gravitational force by a factor of 16.
Explanation:
The gravitational force acting between two objects is directly proportional to the product of mass of the objects and inversely proportional to the square of the distance between the two objects. This is stated by universal law of gravity.
[tex]F=\frac{GmM}{d^{2} }[/tex]
Here M,m are the masses of objects and d is the distance of separation. As the question has stated only increase by a factor of 3 , so i have considered that the increase is of distance by a factor of 3. As force is inversely proportional to the square of the distance(d) , so if the distance increases by factor 3, the gravitational force will be decreased by a factor of 9.
Similarly, if distance d increases by factor of 4, then the square of this term i.e. 16 times the gravitational force will decrease. Thus, increase of distance by a factor of 3 decreases the gravitational force by a factor of 9 and increase of distance by a factor of 4 decreases the gravitational force by a factor of 16.
