Answer:
a) When the connecting rod is massless, the center of mass (CM) of the system is located at the point where the two masses are joined. Therefore, the distance of the CM from m1 is 0.8 m.
b) When the connecting rod is a uniform rod of mass 15 kg, the position of the CM of the system can be found using the parallel axis theorem. The formula for the parallel axis theorem is:
CM = (m1d1 + m2d2 + m3*d3)/(m1 + m2 + m3)
where m1, m2, and m3 are the masses of the two masses and connecting rod, respectively, and d1, d2, and d3 are the distances of their respective CM from the reference point.
In this case, m1 = 15 kg, m2 = 25 kg, m3 = 15 kg, d1 = 0, d2 = 0.8 m, and d3 = 0.4 m (half of the length of the connecting rod).
Substituting these values into the formula, we get:
CM = (150 + 250.8 + 15*0.4)/(15 + 25 + 15) = 0.48 m
So the distance of the CM of the system from m1 is 0.48 m.