A1.8-m uniform rod is being used to balance two buckets of paint. one pucket is full, but the other is mostly empty, and has only 0.25 the inertia of the full bucket. how far away from the full bucket is the center of mass of the system located?

0.36 m

Explanation:

By definition, the x coordinate of the center of mass of the system obeys the following equation:

Xm = (m1x1 + m2x2 + …….+ mnxn) / m1+m2 +……+ mn

Neglecting the mass of the rod, and choosing our origin to be coincident with the location of the full bucket, we can write the following expression for the X coordinate of the center of mass (Assuming that both masses are aligned over the x-axis, so y-coordinates are zero):

Xm = 0.25 mb . 1.8 m / (1+0.25) mb

Simplifying mb, we get:

Xm= 0.36 m (to the right of the full bucket).