Introduction:
In this question, we are given the circular divisions of a screw gauge as 50. We need to find the diameter of the ball based on the given information.

Given:
- Circular divisions of the screw gauge: 50
- Movement on the main scale in one rotation: 0.5mm

Calculating the Pitch:
The pitch is the distance moved by the screw gauge in one complete rotation. We can calculate the pitch using the formula:

Pitch = Distance moved on the main scale / Number of circular divisions

In this case, the distance moved on the main scale in one rotation is 0.5mm and the number of circular divisions is 50. Plugging in these values, we get:

Pitch = 0.5mm / 50 = 0.01mm

Calculating the Diameter:
The diameter of the ball can be calculated using the formula:

Diameter = Pitch x Number of rotations

Since the given information does not mention the number of rotations, we need to make an assumption. Let's assume that the screw gauge has made one complete rotation. Plugging in the values, we get:

Diameter = 0.01mm x 1 = 0.01mm

Therefore, the diameter of the ball is 0.01mm.

Explanation:
A screw gauge is a measuring instrument used to measure the diameter of small objects with high precision. It consists of a main scale and a screw mechanism with a ball at the end. The circular divisions on the screw gauge help in accurately measuring the distance moved by the screw in one rotation.

To find the diameter of the ball, we first calculate the pitch, which is the distance moved by the screw gauge in one complete rotation. This can be calculated by dividing the distance moved on the main scale by the number of circular divisions.

Once we have the pitch, we can calculate the diameter by multiplying the pitch by the number of rotations. However, since the given information does not mention the number of rotations, we need to make an assumption. In this case, we assumed that the screw gauge has made one complete rotation.

By plugging in the values and performing the calculations, we find that the diameter of the ball is 0.01mm.

Conclusion:
The diameter of the ball in the given screw gauge is 0.01mm. This measurement is obtained by calculating the pitch, which is the distance moved by the screw gauge in one complete rotation, and assuming one complete rotation of the screw. The circular divisions on the screw gauge help in accurately measuring the distance moved by the screw.