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To determine the radius of gyration of the complete system, we can use the formula for the radius of gyration of a system of particles:

k^2 = (Σmi * ri^2) / Σmi

Where:
k = radius of gyration of the complete system
mi = mass of each particle
ri = radius of each particle

First, we need to calculate the moment of inertia of each particle about the center of the pulley:

For the 4.5kg mass at 650mm radius:
I1 = m1 * r1^2
I1 = 4.5 * (0.65)^2
I1 = 1.8225 kgm^2

For the 7kg mass at 600mm radius:
I2 = m2 * r2^2
I2 = 7 * (0.6)^2
I2 = 2.52 kgm^2

For the 9kg mass at 250mm radius:
I3 = m3 * r3^2
I3 = 9 * (0.25)^2
I3 = 0.5625 kgm^2

For the 11kg mass at 750mm radius:
I4 = m4 * r4^2
I4 = 11 * (0.75)^2
I4 = 6.1875 kgm^2

Now, we can calculate the total moment of inertia of the system:

ΣI = I1 + I2 + I3 + I4
ΣI = 1.8225 + 2.52 + 0.5625 + 6.1875
ΣI = 11.0925 kgm^2

Now, we can calculate the total mass of the system:

Σm = m1 + m2 + m3 + m4
Σm = 4.5 + 7 + 9 + 11
Σm = 31.5 kg

Finally, we can calculate the radius of gyration of the complete system:

k^2 = ΣI / Σm
k^2 = 11.0925 / 31.5
k^2 = 0.352

k = √0.352
k ≈ 0.593 m

Therefore, the radius of gyration of the complete system is approximately 0.593 meters.