Two full turns of the circular scale of screw gauge cover a distance of $1\,mm$ on scale. The total number of divisions on circular scale is $50$. Further, it is found that screw gauge has a zero error of $+0.03\,mm$. While measuring the diameter of a thin wire a student notes the main scale reading of $3\,mm$ and the number of circular scale division in line, with the main scale is $35$. The diameter of the wire is .......... $mm$

In a Screw Gauge, fifth division of the circular scale coincides with the reference line when the ratchet is closed. There are $50$ divisions on the circular scale, and the main scale moves by $0.5 \,{mm}$ on a complete rotation. For a particular observation the reading on the main scale is $5\, {mm}$ and the $20^{\text {th }}$ division of the circular scale coincides with reference line. Calculate the true reading. (in ${mm}$)

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

In finding out refractive index of glass slab the following observations were made through travelling microscope $50$ vernier scale division $=$ $49 \mathrm{MSD} ; 20$ divisions on main scale in each $\mathrm{cm}$ For mark on paper

$\mathrm{MSR}=8.45 \mathrm{~cm}, \mathrm{VC}=26$

For mark on paper seen through slab

$\mathrm{MSR}=7.12 \mathrm{~cm}, \mathrm{VC}=41$

For powder particle on the top surface of the glass slab

$\mathrm{MSR}=4.05 \mathrm{~cm}, \mathrm{VC}=1$

$(\mathrm{MSR}=$ Main Scale Reading, $\mathrm{VC}=$ Vernier Coincidence)

Refractive index of the glass slab is:

$N$ divisions on the main scale of a vernier calliper coincide with $(N + 1 )$ divisions of the vernier scale. If each division of main scale is $a$ units , then the least count of the instrument is

A screw gauge gives the following reading 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 of the circular scale. The diameter of wire from the above data is: