Open Loop Transfer Function:
The open-loop transfer function of a control system is the transfer function obtained by removing the feedback loop from the system. In this case, the open-loop transfer function is given as:

G(s) = 2(1 - s) / s^2

Gain Margin:
The gain margin is a measure of the system's stability and indicates how much the system's gain can be increased before it becomes unstable. It is defined as the amount of gain at the frequency where the phase of the open-loop transfer function is -180 degrees.

Phase of the Open Loop Transfer Function:
To determine the gain margin, we first need to find the frequency at which the phase of the open-loop transfer function is -180 degrees.

The phase of the open-loop transfer function can be calculated as follows:

Phase = angle(2(1 - s) / s^2)

To find the frequency at which the phase is -180 degrees, we set the phase equal to -180 degrees and solve for s:

-180 = angle(2(1 - s) / s^2)

Finding the Gain Margin:
Once we have found the frequency at which the phase is -180 degrees, we can calculate the gain margin.

The gain margin is given by the reciprocal of the magnitude of the open-loop transfer function at the frequency where the phase is -180 degrees:

Gain Margin = 1 / |G(jω)|

where ω is the frequency at which the phase is -180 degrees.

In this case, since the open-loop transfer function is a rational function, we can substitute jω for s to determine the frequency at which the phase is -180 degrees.

By substituting jω for s in the open-loop transfer function G(s), we can calculate the magnitude of G(jω) at the frequency where the phase is -180 degrees:

|G(jω)| = |2(1 - jω) / (jω)^2|

Simplifying this expression, we get:

|G(jω)| = |2(1 - jω) / -ω^2|

To find the gain margin, we substitute -180 degrees for the phase, calculate the magnitude of the open-loop transfer function at that frequency, and take the reciprocal:

Gain Margin = 1 / |G(jω)|

By performing the calculations, we find that the gain margin is 0.

Therefore, the correct answer is option 'B', 0.