The center of mass is defined as a point on the straight line between two objects with masses m1 and m2 such that l1 / l2 = m2 /m1 . what are the coordinates of the center of mass?

We can represent the problem as shown in the attached drawing

L1=x1

L2=x2

L=x------------distance of the center of mass

we have that

L1/L2=m2/m1------------------> L1*m1=L2*m2------------->m2=L1*m1/L2

moment = Md

the moment about O is defined to be

m1*L1+m2*L2=(m1+m2)*L

L=(m1*L1+m2*L2)/(m1+m2)

m1*L1+m2*L2=2*m1*L1--------remember-------------------->L1*m1=L2*m2

L=(2*m1*L1)/(m1+L1*m1/L2)

L=(2*m1*L1)/(m1*L2+L1*m1)/L2=(2*m1*L1)*L2/(L2*m1+L1*m1)

L=(2*L1*L2)/(L1+L2)

option a.

step-by-step explanation:

if you look closely at the graph, we can notice that the function is not defined at two different points.

if you look at functions b and c, you will notice that both functions are not defined at just one point. the function b is not defined at x= -5/2 and function c is not defined at x=-5. both options are discarded, given that our function should not be defined at two fiferent points.

now, if you look closely at the graph you will notice that the function sketched is not defined at x=5 and x=-2.