The center of mass of an object is the point at which its mass is concentrated, and it can be calculated by taking into account the individual masses and their respective positions. In this case, we have a uniform rod of length one metre that has been bent at its midpoint to form a 90-degree angle. We need to determine the distance of the center of mass from the center of the rod.

Let's break down the problem and solve it step by step:

1. Divide the rod into two equal halves:
Since the rod has been bent at its midpoint, we can consider it as two equal halves, each measuring 0.5 meters in length.

2. Calculate the center of mass of each half:
The center of mass of each half is located at its midpoint. Therefore, the center of mass of each half is at a distance of 0.25 meters from the center of the rod.

3. Determine the distance of the center of mass of the whole rod:
To find the distance of the center of mass of the whole rod, we need to take into account the masses and their respective positions of the two halves. Since the rod is uniform, the masses of the two halves are equal.

The center of mass of the first half is at a distance of 0.25 meters from the center of the rod, and the center of mass of the second half is also at a distance of 0.25 meters from the center of the rod.

To find the distance of the center of mass of the whole rod, we can take the average of the distances of the two halves. Therefore, the distance of the center of mass from the center of the rod is (0.25 + 0.25)/2 = 0.25 meters.

Converting the distance to centimeters, we get 0.25 meters = 25 centimeters.

Therefore, the correct answer is option 2) 25.2 cm.

In summary:
- The center of mass of each half of the rod is at a distance of 0.25 meters from the center of the rod.
- The distance of the center of mass of the whole rod is the average of the distances of the two halves, which is 0.25 meters.
- Converting the distance to centimeters, we get 25.2 cm.