Under many conditions, the center of mass of a system of particles can represent the system as a whole. But how far does this rule extend?

Consider two identical particles traveling toward each other at the same speed. By examining this system, choose the correct response.

a. The momentum and kinetic energy of the center of mass is equivalent to that of the system of particles.
b. The kinetic energy, but not the momentum, of the center of mass is equivalent to that of the system of particles.
c. Neither the momentum nor the kinetic energy of the center of mass is equivalent to that of the system of particles.
d. The momentum, but not the kinetic energy, of the center of mass is equivalent to that of the system of particles.

The correct answer is a

Explanation:

The concept of center of mass strongly simplifies the analysis of problems, since all the external bridging forces = denote the point of the center ce plus.

                 xcm = 1 / M ∑xi mi

                 v cm = 1 / M ∑ xi vi

When we do this, the momentum and the kinetic energy are conserved, that is, it is equivalent to the movement of the particle system

The correct answer is a

The value of r is

Explanation:

Generally for a series connection the equivalent resistance is mathematically evaluated as

Where are and are given in the question

The current is mathematically  represented as

Generally for a parallel connection the equivalent resistance is mathematically evaluated as  

The current is mathematically  represented as                

Now we are told that  

                                           =>    

                                           =>    

                                           =>    

From the question

Substituting this into the equation we have

Multiplying through by r

Solving the equation using quadratic formula

Now recall the so

Hence