Laws of Motion
6.0 Gravitional Force
6.0 Gravitional Force
The force on one body due to another, which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
Mathematically, the magnitude of this force is given by, $$F = G\frac{{{m_1}{m_2}}}{{{r^2}}}$$
The above formula was formulated by Sir Issac Newton.
The weight of the body on the surface of the earth is equal to the gravitational pull acting on body towards its center.
Mathematically, it is given by, $$F = G\frac{{{M_e}m}}{{{R^2}}}\quad ...(i)$$
where,
$M_e$: Mass of the earth
$m$: Mass of the body
$G$: Universal gravitational constant
$R$: Radius of the earth
Acceleration due to gravity $(g)$
It is equal to the force experienced by a unit mass on the earth’s surface.
It is given by, $$g = G\frac{{{M_e}}}{{{R^2}}}\quad \left( {As,\;m = 1} \right)\quad ...(ii)$$
From equation $(i)$ and $(ii)$ we get, $$F = mg$$
The weight of the body always acts at the center of gravity of a body.
For a uniform symmetric body, the center of gravity of a body is at its center.
Centre of gravity: It is a point where we consider the total gravitational force to be acting.
Centre of mass: It is a point where we consider the total mass of the body to be present.
If the body is uniform and symmetric, then the center of gravity and center of mass are at the same point.
For a uniform symmetric body, the center of gravity of a body is at its center.
