Question

The following table gives the range of a particle when thrown on different planets. All the particles are thrown at the same angle with the horizontal and with the same initial speed. Arrange the planets in ascending order according to their acceleration due to gravity, (g value).
Planet Range
Jupiter 50 m
Earth 75 m
Mars 90 m
Mercury 95 m

Answer 1

For a Projectile Motion, Range is given by:

$R = \frac{u^2 \sin 2\theta}{g}$

Here

$u$ = Velocity of projection
$\theta$ = Angle of projection
$g$ = Gravitational acceleration

Here we see that Range is inversely proportional to gravitational acceleration.


This means that the planets which have larger values of g will have lower values of Range, and vice-versa.

Now, 
Decreasing Order of Range is:

$\begin{array}{cc} Mercury & 95 \, \, m \\ Mars & 90 \, \, m \\ Earth & 75 \, \, m \\ Jupiter & \, \, 50 \, \, m \end{array}$


Decreasing Order of Range shows the increasing order of g.


So, ascending order of planets according to the value of g is:

Mercury < Mars < Earth < Jupiter

Answer 2

Range is the horizontal distance the projectile would cover.
Range of any projectile is inversely proportional to the acceleration due to gravity at that place.
Higher range implies lower acceleration due to gravity.
So, the order of acceleration due to gravity would be Mercury<Mars<Earth<Jupiter