One main scale division of a vernier caliper is equal to $m$ units. If $n^{\text {th }}$ division of main scale coincides with $(n+1)^{\mathrm{th}}$ division of vernier scale, the least count of the vernier caliper is:

A vernier callipers has $20$ divisions on the vernier scale, which coincides with $19^{\text {th }}$ division on the main scale. The least count of the instrument is $0.1 \mathrm{~mm}$. One main scale division is equal to $. . .  . . ..$ $\mathrm{mm}$

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 ${mm}$)

If the screw on a screw-gauge is given six rotations, it moves by $3\; \mathrm{mm}$ on the main scale. If there are $50$ divisions on the circular scale the least count of the screw gauge is

A screw gauge of pitch $0.5\,mm$ is used to measure the diameter of uniform wire of length $6.8\,cm$, the main scale reading is $1.5\,mm$ and circular scale reading is $7$. The calculated curved surface area of wire to appropriate significant figures is $......cm^2$ . [Screw gauge has $50$ divisions on the circular scale]

The pitch and the number of divisions, on the circular scale, for a given screw gauge are $0.5\,mm$ and $100$ respectively. When the screw gauge is fully tightened without any object, the zero of its circular scale lies $3$ divisions below the mean line. The readings of the main scale and the circular scale for a thin sheet, are $5.5\,mm$ and $48$ respectively, the thickness of this sheet is