A

Step 1: Identify the conversion factors between the CGS (centimeter-gram-second) system and the new system (kilogram-meter-minute).
1 dyne = 10^{-5} N (Newton) in SI units.
Step 2: Therefore, the magnitude of the force in Newtons in the SI system is:
100 \, dynes = 100 \, \times \, 10^{-5} \, N = 1 \, \times \, 10^{-3} \, N.
Step 3: Convert Newtons to the new system. The unit of force in the new system is based on kilogravity; 1 N = 1 \frac{kg \, m}{s^2}.
Step 4: We need to relate the acceleration due to gravity in this new system using minutes and converting it accordingly.
(Since the system uses minutes, we calculate force as follows):
Acceleration due to gravity, g \approx 980 \, cm/s^2 = 9.8 \, m/s^2 = 9.8 \, \frac{m}{(60 \times 60)^2} = 9.8 * 3600 \, m/m^2 = 9.8 * 3600 \, \frac{m}{s^2}.
Step 5: The conversion gives us the force in this system:
F = m \, g, where m is in kg, g is in \frac{m}{min^2}.
Step 6: Substituting values, we calculate:
F = 1 \times 10^{-3} \cdot 1 = 0.036 \cdot (kg \cdot m/min^2).
Therefore, the magnitude of the force in the new system is approximately 0.036.
Thus, the correct answer is Option A.