A screw gauge gives the following readings when used to measure the diameter of a wire

Main scale reading : 0 mm

Circular scale reading : 52 divisions

Given that 1 mm on main scale corresponds to 100 divisions on the circular scale.

The diameter of the wire from the above data is :

To find the diameter of the wire, we need to calculate the least count of the screw gauge and then use the readings to determine the total measurement.

Step 1: Understand the given parameters
Main scale reading (MSR) = $0\text{mm}$
Circular scale reading (CSR) = $52\text{divisions}$
Pitch of the screw gauge (the distance corresponding to one full rotation or the smallest division on the main scale) = $1\text{mm}$
Total number of circular scale divisions = $100$

Step 2: Calculate the Least Count (LC) of the screw gauge
The least count is the smallest value that can be measured accurately by the instrument, calculated as:
$\text{Least Count (LC)}=\frac{\text{Pitch}}{\text{Total circular scale divisions}}$
Substituting the given values:
$\text{LC}=\frac{1\text{mm}}{100}=0.01\text{mm}$

Step 3: Calculate the measured diameter
The formula for the total reading (diameter) is:
$\text{Total Reading}=\text{Main Scale Reading (MSR)}+(\text{Circular Scale Reading (CSR)}\times \text{Least Count (LC)})$
Substituting the values we have:
$\text{Diameter}=0\text{mm}+(52\times 0.01\text{mm})$
$\text{Diameter}=0.52\text{mm}$

Step 4: Convert the diameter to centimeters (cm)
Since the options are given in centimeters, we convert millimeters to centimeters by dividing by $10$ (since $1\text{cm}=10\text{mm}$):
$\text{Diameter}=\frac{0.52}{10}\text{cm}=0.052\text{cm}$

Therefore, the correct diameter of the wire is 0.052 cm.