Question

What is acceleration of the first particle relative to the second?

Answer 1

A body which is moving upward, is said to experience free fall, if only force due to gravity is acting on the body. Here, since there is no external force on the body, the body experiences free fall. Where only acceleration due to gravity is acting on the body.

Complete step by step answer:
We know from Newton's law of gravitational law, that every particle attracts every other particle in the universe with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres. This is a general physical law derived from empirical observations by what Isaac Newton called inductive reasoning. This was the basis Kepler’s laws of planet motion are three scientific laws describing the motion of planets around the Sun.
We know that the gravitational force is a non-contact force. We know that according to Newton-Kepler law of gravitation, gravitational force is given as, the force due to gravitation is given as $F=G\dfrac{m_{1}m_{2}}{r^{2}}$, where $G$ is the gravitational constant, $m_{1},m_{2}$ is the masses of the body, and $r$ is the distance between the two bodies.
From gravitational law, we know $g=\dfrac{GM}{R^2}$ we also know that gravity at any height is given by $g_{h}= g\left(1+\dfrac{h}{R}\right)^{-2}$ where $g_{h}$ the gravity at $h$ and $R$ is the radius of the earth.
Let us assume that we have two balls of mass $m_{1},m_{2}$ respectively which experience free fall from some height $h$, then clearly, the only acceleration they experience us acceleration due to gravity $g$ which is independent of the mass of the body and is a constant, then we can also say that the relative acceleration of the body is zero.

Note: Acceleration due to gravity $g$ has a negative sign, as it tends to draw the ball towards the earth. Free fall results in weightlessness, where the mass of the body does not affect the motion of the body. Thus, you may notice that the mass of the body is not given here.