b) Show that the center of mass for this configuration always has its center of mass at 50 cm mark, no matter the value of N.As we discussed in class, a meter stick can be approximated by discrete set of masses connected by a massless rod. For a uniform meter stick, we can assume that all masses are the same and they are equally spaced. For example, if the meter stick is composed by N total particles, where N is a large whole number, each one will have mass M /N (where M is the total mass of the ruler) and the space between adjacent particles will be 1 / (N 1) meters. a) If we align the meter stick with the :1: axis and set the origin to be at the point were the ruler marks 0cm, nd the mass and the position of the kth particle. (Hint: Start with simpler cases, such as N = 2, 3, 4 and then try to generalize it to general N) Analogously to the previous problem, let us now approximate an inhomogenous 12inch ruler by 13 massive particles connected through 1inch massless rods. Since the ruler is not uniform, the particles must have different masses. Assuming that the ruler mass is distributed such that the k-th particle has mass M Z k m'\" 91 ' nd the center of mass of the ruler