Given data
*The given mass of the space rock is m = 5.0 kg
*The given mass of the Earth is M = 6.0 × 10^24 kg
*The separation distance is r = 2.5 × 10^7 m
*The value of the gravitational constant is G = 6.67 × 10^-11 N.m^2/kg^2
(A)
The formula for the force of gravity acting on the space rock, due to the Earth is given as
[tex]F=\frac{GmM}{r^2}[/tex]Substitute the known values in the above expression as
[tex]\begin{gathered} F=\frac{(6.67\times10^{-11})(5.0)(6.0\times10^{24})}{(2.5\times10^7)^2} \\ =3.2\text{ N} \end{gathered}[/tex]Hence, the force of gravity acting on the space rock, due to the Earth is F = 3.2 N
(B)
The expression for the acceleration of the rock would experience is given as
[tex]\begin{gathered} F=ma \\ a=\frac{F}{m} \end{gathered}[/tex]Substitute the known values in the above expression as
[tex]\begin{gathered} a=\frac{3.2}{5} \\ =0.64m/s^2 \end{gathered}[/tex]Hence, the acceleration the rock would experience is a = 0.64 m/s^2
