91Ó°ÊÓ

The figure for three particle system initially fixed in place, with B and C identical and positioned symmetrically about y-axis at distance from A.

The force of attraction between any two bodies is directly proportional to the product of their masses and is inversely proportional to the square of the distance between them, according to Newton's universal law of gravitation.Using the concept of the vector diagram, we can find the direction of the net force as per the given conditions.

Formula:

The Gravitational force of attraction between two bodies of masses M and m separated by distance R is, $F=\frac{GMm}{R^2}$ …(¾±)

Free body diagram:

From the above vector diagram, we can conclude that the direction of the net gravitational force ${\stackrel{→}{F}}_{net}$on A is along +y direction.

As C is moved away from the origin, the gravitational force ${\stackrel{→}{F}}_{AC}$on A will decrease with distance. This is because force is inversely proportional to the square of a distance between the masses according to equation (i). So as C moves away, the net force would move towards B as force exerted by the particle at B on A would become greater than that of the particle at C.

At infinity, the value of force because the particle is at C would become zero and the net force would be the only force exerted by particle B on A.

Therefore, as particle C moves away to infinity, value of ${\stackrel{→}{F}}_{net}$would decrease till it becomes equal to ${\stackrel{→}{F}}_{AB}$.