Question

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?

Answer 1

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)

the coordinates of the center of mass are (L,0)