Final answer:
To find the ratio of their period of oscillation, use the formula T = 2π√(m/k) for each spring and calculate the ratio T1/T2 by simplifying the respective time periods.
Step-by-step explanation:
The question involves determining the ratio of periods of oscillation for two springs with different stiffness values, each carrying a load. The oscillation period (T) for a spring-mass system in simple harmonic motion is given by the formula T = 2π√(m/k), where m is the mass of the load and k is the spring constant or stiffness.
For the first spring with a stiffness of 0.04 N/m:
T1 = 2π√(4.0 kg / 0.04 N/m)
For the second spring with a stiffness of 1.6 N/m:
T2 = 2π√(4.0 kg / 1.6 N/m)
The ratio of their periods T1/T2 can be calculated by dividing the formulas, simplifying, and comparing the results to the given options.