Answer:
The new force of attraction would be 36 units
Explanation:
Law of Universal Gravitation
Objects attract each other with a force that is proportional to their masses and inversely proportional to the square of the distance.
This statement can be expressed with the formula:
[tex]\displaystyle F=G{\frac {m_{1}m_{2}}{r^{2}}}[/tex]
Where:
m1 = mass of object 1
m2 = mass of object 2
r = distance between the objects' center of masses
G = gravitational constant: [tex]6.67\cdot 10^{-11}~Nw*m^2/Kg^2[/tex]
Now suppose two given objects attract with a force of F=16 units, thus:
[tex]\displaystyle G{\frac {m_{1}m_{2}}{r^{2}}}=16[/tex]
And now the masses of both objects is tripled, i.e., m1'=3m1, m2'=3m2, and the distance between them is doubled, r'=2r. The new force is:
[tex]\displaystyle F'=G{\frac {3m_{1}3m_{2}}{(2r)^{2}}}[/tex]
Operating:
[tex]\displaystyle F'=G{\frac {9m_{1}m_{2}}{4r^{2}}}[/tex]
[tex]\displaystyle F'=\frac{9}{4}G{\frac {m_{1}m_{2}}{r^{2}}}[/tex]
Substituting the value of the initial force:
[tex]\displaystyle F'=\frac{9}{4}\cdot 16[/tex]
[tex]F'=36\ units[/tex]
The new force of attraction would be 36 units
