Introduction:
In the International System of Units (SI), force is measured in newtons (N). To determine the number of newtons contained in a unit of force in a particular system of measurement, we need to understand the relationship between force and other fundamental units.

Relationship between force and fundamental units:
Force can be defined as the product of mass and acceleration. In SI units, mass is measured in kilograms (kg) and acceleration is measured in meters per second squared (m/s²). Therefore, the unit of force in SI is kg⋅m/s², which is equivalent to one newton (N).

Determining the number of newtons in a unit of force:
To determine the number of newtons contained in a unit of force in a particular system of measurement, we need to express the fundamental units of length, mass, and time in terms of SI units and then calculate the value of force in newtons.

Given that the unit of length is 5cm, mass is 100g, and time is 0.01sec, we can convert these values to SI units as follows:

- Length: 5cm = 0.05m
- Mass: 100g = 0.1kg
- Time: 0.01sec = 0.01s

Using these values, we can calculate the value of force in SI units as follows:

- Force = mass × acceleration
- Acceleration = length / time²
- Acceleration = 0.05m / (0.01s)² = 50m/s²
- Force = 0.1kg × 50m/s² = 5N

Therefore, the unit of force in this system of measurement contains 5 newtons (N).

Conclusion:
In conclusion, to determine the number of newtons contained in a unit of force in a particular system of measurement, we need to express the fundamental units of length, mass, and time in terms of SI units and then calculate the value of force in newtons using the formula F = ma. In the given system of measurement, the unit of force contains 5 newtons (N).