The time period of a pendulum is given by the formula T = 2π√(L/g), where T is the time period, L is the length of the pendulum, and g is the acceleration due to gravity.

Let's analyze the given scenario step by step:

1. Pendulum in space laboratory:
The pendulum is placed in a space laboratory, which means it is in a microgravity environment. In microgravity, the acceleration due to gravity is significantly reduced compared to the surface of the Earth. Therefore, the value of g will be much smaller.

2. Orbiting around the Earth:
The space laboratory is orbiting around the Earth at a height of 3R, where R is the radius of the Earth. In this scenario, the pendulum is not in contact with the Earth's surface, and the gravitational force acting on it will be weaker than on the surface.

3. Length of the pendulum:
The length of the pendulum remains the same, regardless of its position. The length is usually measured from the point of suspension to the center of mass of the pendulum bob.

Now, let's consider the effects of these factors on the time period of the pendulum:

- Reduction in acceleration due to gravity (g):
Since the pendulum is in a microgravity environment, the value of g will be much smaller than on the surface of the Earth. As a result, the time period of the pendulum will increase.

- Weaker gravitational force:
The gravitational force acting on the pendulum will be weaker than on the surface of the Earth. This weaker force will result in a longer time period.

- Unchanged length of the pendulum:
The length of the pendulum remains the same, regardless of its position. Therefore, it does not affect the time period of the pendulum.

Considering the above factors, it can be concluded that the time period of the pendulum in the given scenario will be infinite. This is because the pendulum is in a microgravity environment with a weaker gravitational force, resulting in a significantly increased time period.