A screw has a pitch equal to 0.5 mm. What should be the number of division on its head so as to read correct up to 0.001mm with its help?

As we know,

$\text {Least count} = \dfrac{\text{Pitch}}{\text{Total no. of div on circular head}} \\[0.5em]$

Given,

Pitch = 0.5 mm

L.C. = 0.001 mm

Substituting the values in the formula above we get,

$0.001\text{mm} = \dfrac{0.5}{\text{Total no. of div on circular head}} \\[0.5em] \Rightarrow \text{Total no. of div on circular head} = \dfrac{0.5}{0.001} \\[0.5em] \Rightarrow \text{Total no. of div on circular head} = 500$

Hence, total number of divisions on circular head = 500.