Question

If symbols have their usual meanings, then which of the following relations is true for equilibrium of a particle?
A. $\dfrac{{du}}{{dr}} = 0$
B. $\dfrac{{du}}{{dr}} > 0$
C. $\dfrac{{du}}{{dt}} < 0$
D. $\dfrac{{du}}{{dr}} = K$ ( $K$ not equal to $0$ )

Answer 1

A particle is considered to be in equilibrium if there is no net force acting on it, according to Newton's first law. This does not imply that no forces act on the particle; rather, it implies that the sum of all forces acting on the particle is zero.

Complete step by step answer:
Equilibrium of a Particle: A particle is said to be in equilibrium when the net external force acting on it is zero. We can state that the particle is either at rest or in uniform motion if we apply Newton's First Law of Motion to this circumstance. When a particle is at rest, it is said to be in static equilibrium, and when the body is moving uniformly, it is said to be in dynamic equilibrium. For equilibrium of particle;
$F = 0 \\\ \therefore \dfrac{{du}}{{dr}} = 0 \\\$
Hence, the correct option is A.

Note: When two forces engage on a particle to keep it in equilibrium, both forces must have the same magnitude but opposite directions, and they must be collinear. Three forces acting on a particle must be coplanar in order to keep it in equilibrium. The third force is equal to and opposite to the resultant of any two forces. The equilibrant force is the name given to the third force. The total of the three forces' vectors must equal zero. The vector sum of the $n$ forces must equal zero when $n$ forces act on a particle to keep it in equilibrium.