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 :

First, identify the least count (smallest division) of the screw gauge.

$1\backslash \; \backslash text\{mm\}=100\backslash \; \backslash text\{divisions\}$

Therefore, the value of one division is

$\backslash text\{least\; count\}=\; \backslash frac\{1\backslash \; \backslash text\{mm\}\}\{100\}=0.01\backslash \; \backslash text\{mm\}$

Convert this to centimeters (1 mm = 0.1 cm):

$0.01\backslash \; \backslash text\{mm\}=0.01\; \backslash times\; 0.1\backslash \; \backslash text\{cm\}=0.001\backslash \; \backslash text\{cm\}$

Now use the reading from the circular scale. The circular scale shows 52 divisions.

$\backslash text\{Contribution\; of\; circular\; scale\}=52\; \backslash times\; 0.001\backslash \; \backslash text\{cm\}=0.052\backslash \; \backslash text\{cm\}$

The main scale reading is 0 mm, so it adds nothing to the total.

Hence the diameter of the wire is

$\backslash text\{Diameter\}=0\backslash \; \backslash text\{mm\}+0.052\backslash \; \backslash text\{cm\}=0.052\backslash \; \backslash text\{cm\}$

Thus the correct answer is **0.052 cm**.