Answer:
Choice: D.
Explanation:
Newton’s Law of Universal Gravitation
It states that objects attract each other with a force that is proportional to their masses and inversely proportional to the square of the distance between them. The formula is:
[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]
The center of mass of a cow is at a distance of r=208 m from the center of the mass of a tractor. The gravitational force of attraction is [tex]F=1.8\cdot 10^{-9}\ N[/tex]. It's required to find the new force of attraction F' if the distance was r'=416 m.
It can be noted that r'=2r. If the distance is doubled, the new force is:
[tex]\displaystyle F'=G{\frac {m_{1}m_{2}}{(2r)^{2}}}[/tex]
[tex]\displaystyle F'=\frac{1}{4}G{\frac {m_{1}m_{2}}{r^{2}}}[/tex]
Substituting the original value of F:
[tex]\displaystyle F'=\frac{1}{4}\cdot 1.8\cdot 10^{-9}\ N[/tex]
Operating:
[tex]\displaystyle F'=4.5\cdot 10^{-10}\ N[/tex]
Choice: D.
