5)
a)
In order to calculate the force acting on the masses, we can use the formula below:
[tex]F=\frac{G\cdot M\cdot m}{d^2}[/tex]
Where G is the gravitational constant (G = 6.674 * 10^-11), M is the greater mass, m is the smaller mass and d is the distance between the masses.
So, for M = 6 * 10^24 kg, m = 1 kg and d = 6.4 * 10^6 m, we have:
[tex]\begin{gathered} F=\frac{6.674\cdot10^{-11}\cdot6\cdot10^{24}\cdot1}{(6.4\cdot10^6)^2} \\ F=\frac{40.044\cdot10^{13}}{40.96\cdot10^{12}} \\ F=9.78\text{ N} \end{gathered}[/tex]
b)
The force calculated in item a) will act on both masses, therefore the force acting on the larger object is also F = 9.78 N.
c)
The acceleration can be calculated using the second law of Newton:
[tex]\begin{gathered} F=m\cdot a \\ 9.78=1\cdot a \\ a=9.78\text{ m/s2} \end{gathered}[/tex]
d)
Using the second law of Newton again, we have:
[tex]\begin{gathered} F=M\cdot a \\ 9.78=6\cdot10^{24}\cdot a \\ a=1.63\cdot10^{-24}\text{ m/s2} \end{gathered}[/tex]
