Solve 13, 14, 15 and 16 questions

Dear student,

16.Mass of particle remains same.Accelleration due to gravity varies because of increase in the distance.
Let height be h,
Surface of the earth 
$$\begin{gathered} 120N=\frac{GMm}{R^2} \\ R, radius of earth \end{gathered}$$

Then at height h then
$F\text{'}=30N=\frac{GMm}{{\left(R+h\right)}^2}$

Dividing the two equation
$$\begin{gathered} 4=\frac{{\left(R+h\right)}^2}{R^2} \\ 2=\frac{\left(R+h\right)}{R} \\ h=R \end{gathered}$$
Thus at height 6400 km.

(15)Let the force on earth be
$F_e=m{g}_e$
Where g_e is gravitational force on earth.
Let force on mercury be
$F_m=m{g}_m$
g_m gravitational force on mercury.
mass remains same on earth and mercury.
$$\begin{gathered} \frac{F_e}{F_m}=\frac{g_e}{g_m} \\ \frac{980}{370}=\frac{9.8}{g_m} \\ {g}_m=3.7m/s^2 \end{gathered}$$


Regards.