To find the force (F) acting on the system, we can use Newton's second law of motion:

F = m1 a1 + m2 a2

Given:
m1 = 0.1 kg
a1 = 4 m/s^2
m2 = 0.5 kg
a2 = 5 m/s^2

Plugging in the values:

F = (0.1 kg 4 m/s^2) + (0.5 kg 5 m/s^2)
F = (0.4 N) + (2.5 N)
F = 2.9 N

Therefore, the force (F) acting on the system is 2.9 Newtons.