Answer: 1.424 N
Explanation:
According to Newton's Universal Law of Gravitation:
[tex]F_{g}=G\frac{(m_{b})(m_{E})}{d^2}[/tex] (1)
Where:
[tex]F_{g}[/tex] is the gravitational force between the ball and Earth
[tex]G=6.674(10)^{-11}\frac{m^{3}}{kgs^{2}}[/tex] the Universal Gravitational Constant
[tex]m_{b}=0.145 kg[/tex] is the mass of the ball
[tex]m_{E}=5.9742 (10)^{24} kg[/tex] is the mass of the Earth
[tex]d=r_{b}+r_{E}[/tex] is the distance between the ball and the Earth, being [tex]r_{b}=0.075 m[/tex] the radius of the ball and [tex]r_{E}=6.3710(10)^{6} m[/tex] the radius of the Earth
So, rewritting (1):
[tex]F_{g}=G\frac{(m_{b})(m_{E})}{(r_{b}+r_{E})^2}[/tex] (2)
[tex]F_{g}=6.674(10)^{-11}\frac{m^{3}}{kgs^{2}}\frac{(0.145 kg)(5.9742 (10)^{24} kg)}{(0.075 m+6.3710(10)^{6} m)^2}[/tex] (3)
Finally:
[tex]F_{g}=1.424 N[/tex] (4)
