State Newton's universal law of gravitation and write an expression for it. Also,show that the acceleration due to gravity of an object is independent of its mass.

(N/A) Newton's universal law of gravitation states that every particle of matter in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
Mathematically,the force $F$ is given by:
$F = \frac{G m_1 m_2}{r^2}$
where $G$ is the universal gravitational constant,$m_1$ and $m_2$ are the masses of the two objects,and $r$ is the distance between their centers.
To show that acceleration due to gravity $(g)$ is independent of the mass of the falling object,consider an object of mass $m$ falling towards the Earth (mass $M$,radius $R$).
The gravitational force is $F = \frac{G M m}{R^2}$.
According to Newton's second law,$F = m \times a$. Here,$a = g$,so $F = m \times g$.
Equating the two expressions: $m \times g = \frac{G M m}{R^2}$.
Canceling $m$ from both sides,we get $g = \frac{G M}{R^2}$.
Since $g$ depends only on the mass of the Earth $(M)$,the gravitational constant $(G)$,and the radius of the Earth $(R)$,it is independent of the mass $(m)$ of the falling object.