To determine the minimum speed required for an object to remain in a stable orbit around a rotating space station, we need to consider the gravitational force and the centrifugal force acting on the object.

The gravitational force, provided by the space station, is given by the equation:

Fg = (G * m * M) / r^2

where:
- Fg is the gravitational force,
- G is the gravitational constant (approximately 6.67430 × 10^-11 N(m/kg)^2),
- m is the mass of the object,
- M is the mass of the space station,
- r is the radius of the space station.

The centrifugal force, due to the rotation of the space station, is given by the equation:

Fc = m * (v^2 / r)

where:
- Fc is the centrifugal force,
- v is the velocity of the object.

In a stable orbit, the gravitational force Fg and the centrifugal force Fc are equal and opposite. Therefore, we can equate them:

(G * m * M) / r^2 = m * (v^2 / r)

Simplifying the equation:

G * M / r = v^2

To find the minimum speed required, we need to consider the situation where the gravitational force is at its strongest, which is at the surface of the space station. At the surface, r is equal to the radius of the space station.

Substituting the values:

G * M / 100 = v^2

Now we can solve for v:

v^2 = G * M / 100

v = sqrt(G * M / 100)

We can calculate the minimum speed required by substituting the values of G and M into the equation:

v = sqrt((6.67430 × 10^-11 N(m/kg)^2) * (mass of space station) / 100)

The mass of the space station is not given in the question, so we cannot calculate the exact minimum speed required without that information.

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