A travelling microscope is used to determine the refractive index of a glass slab. If $40$ divisions are there in $1 \; cm$ on main scale and $50$ Vernier scale divisions are equal to $49$ main scale divisions, then least count of the travelling microscope is $\dots \; \times 10^{-6} \; m$

The least count of the main scale of a screw gauge is $1\, mm$. The minimum number of divisions on its circular scale required to measure $5\,\mu m$ diameter of a wire is

The figure of a centimetre scale below shows a particular position of the Vernier calipers. In this position, the value of $x$ shown in the figure is .......... $cm$ (figure is not to scale)

The vernier scale used for measurement has a positive zero error of $0.2\, mm$. If while taking a measurement it was noted that $'0'$ on the vernier scale lies between $8.5\, cm$ and $8.6\, cm$ vernier coincidence is $6,$ then the correct value of measurement is ............. $cm$. (least count $=0.01\, cm )$

One main scale division of a vernier callipers is $a$ $cm$ and $n ^{\text {th }}$ division of the vernier scale coincide with $( n -1)^{\text {th }}$ division of the main scale. The least count of the callipers in $mm$ is