The acceleration of the center-of-mass point of a system of particles depends on:
a) all the forces acting on the system
b) only the external forces acting on the system
c) only the internal forces acting on the system
To determine the answer to this question, let's consider the definition of the center of mass and the principles of Newtonian mechanics.
The center of mass of a system of particles is the point at which the system's mass can be considered to be concentrated. It can be calculated by taking the weighted average position of all the particles, where the weights are given by the masses of the particles.
According to Newton's second law of motion, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Mathematically, this can be expressed as F = ma, where F is the net force, m is the mass, and a is the acceleration.
Considering these principles, the acceleration of the center-of-mass point of a system of particles depends on the net force acting on the system and the total mass of the system. Therefore, the correct answer is:
b) only the external forces acting on the system
Internal forces cancel out in a system of particles because every force exerted by one particle on another is accompanied by an equal and opposite force exerted by the second particle on the first. As a result, the net force due to internal forces is zero, and they do not contribute to the acceleration of the center of mass. Only the external forces, such as those applied by external objects or gravitational forces from outside the system, affect the acceleration of the center of mass.