For the system of particles described in the part b, find the x coordinate xcm of the center of mass. assume that the particle of mass m is at the origin and the positive x axis is directed to the right. express your answer in terms of l.

for mass M, x_cm = 1.33 L

for mass 2M, x_cm = 0.33 L

for mass 3M, x_cm = 0.67 L

Explanation:

The system of mass image in the attachment

The x-coordinate of the mass center from the mass M

             x_{cm} = [ M(0) + (2M)L + (3M)(2L) ]÷(M + 2M + 3M)

                    = [ 2LM + 6LM ] / (6M)

                    = 1.33 L

The x-coordinate of mass center from the mass 2M is

             x_{cm} = [ M(-L) + (2M)(0) + (3M)(L) ] ÷ (M + 2M + 3M)

                    = [ - LM + 3LM ] / (6M)

                    = 0.33 L

The x-coordinate of mass center from the mass 3M is

             xcm = [ M(-2L) + (2M)(-L) + (3M)(0) ]÷(M + 2M + 3M)

                    = [ - 2LM - 2LM ] / (6M)

                    = 0.67 L

this allows people to make the best decision or pursue the best option. when alternatives are weighed using their advantages and disadvantages, the option whose disadvantages outweigh the advantages (based on a qualitative or quantitative analysis) are shunned while those whose advantages outweigh their disadvantages are pursued.