Answer: D) It would be cut in half.
Explanation:
According to Newton's law of universal gravitation we have the following:
[tex]F=G\frac{m_{1}m_{2}}{r^2}[/tex] (1)
Where:
[tex]F[/tex] is the module of the attraction force exerted between both bodies
[tex]G[/tex] is the universal gravitation constant.
[tex]m_{1}[/tex] is the mass of the backyard and [tex]m_{2}[/tex] is the mass of the boulder
[tex]r[/tex] is the distance between the backyard and the bouder
Now, if the mass of the boulder were half the mass, equation (1) would be:
[tex]F=G\frac{m_{1}\frac{m_{2}}{2}}{r^2}[/tex] (2)
[tex]F=\frac{1}{2} G\frac{m_{1}\m_{2}{2}}{r^2}[/tex] (3)
Comparing (1) and (2) we can see the gravitational force is reduced to a half.
Hence, the correct option is D: