Using screw gauge of pitch 0.1 cm and 50 divisions on its circular scale, the thickness of an object is measured. It should correctly be recorded as:

We are dealing with a screw gauge. The very first thing to note is its pitch and the number of divisions on its circular scale.

The statement gives us

$$\text{Pitch}=0.1\ \text{cm}$$

and

$$\text{Number of circular scale divisions}=50.$$

For any screw gauge the smallest length it can measure - that is, the least count - is given by the standard relation

$$\text{Least Count}=\frac{\text{Pitch}}{\text{Number of divisions on circular scale}}.$$

Substituting the given values, we obtain

$$\text{Least Count}= \frac{0.1\ \text{cm}}{50} = 0.002\ \text{cm}.$$

This value tells us that every reading taken with this screw gauge must differ from the next possible reading by an exact multiple of $$0.002\ \text{cm}.$$ In simpler words, any valid final answer has to end in the thousandths place such that the last three-digit block is a multiple of 2 in the third decimal.

Now we inspect the four options:

$$\begin{aligned} \text{Option A:}&\;2.121\ \text{cm}\\ \text{Option B:}&\;2.124\ \text{cm}\\ \text{Option C:}&\;2.125\ \text{cm}\\ \text{Option D:}&\;2.123\ \text{cm} \end{aligned}$$

We test each by subtracting the integer part and checking divisibility by the least count:

$$2.121-2.000 = 0.121\ \text{cm},\quad\frac{0.121}{0.002}=60.5\;(\text{not an integer}).$$

$$2.124-2.000 = 0.124\ \text{cm},\quad\frac{0.124}{0.002}=62\;(\text{exact integer}).$$

$$2.125-2.000 = 0.125\ \text{cm},\quad\frac{0.125}{0.002}=62.5\;(\text{not an integer}).$$

$$2.123-2.000 = 0.123\ \text{cm},\quad\frac{0.123}{0.002}=61.5\;(\text{not an integer}).$$

Only Option B, $$2.124\ \text{cm},$$ is an exact multiple of the least count and therefore respects the precision of the screw gauge.

Hence, the correct answer is Option B.