$1\,M.S.D. = 100\, C.S.D. = 1\, mm $ 
Main scale reading : $0 \,\mathrm{~mm}$
Circular scale reading $: 52$ $divisions$
Given that $1\, \mathrm{~mm}$ on main scale corresponds to $100\, divisions$ on the circular scale. The diameter of the wire from the above data is ...... $cm$
$(A)$ $\alpha+p=2 \beta$
$(B)$ $p+q-r=\beta$
$(C)$ $p-q+r=\alpha$
$(D)$ $p+q+r=\beta$