There are $100$ divisions on the circular scale of a screw gauge of pitch $1 \mathrm{~mm}$. With no measuring quantity in between the jaws, the zero of the circular scale lies $5$ divisions below the reference line. The diameter of a wire is then measured using this screw gauge. It is found the $4$ linear scale divisions are clearly visible while $60$ divisions on circular scale coincide with the reference line. The diameter of the wire is :

A specially designed Vernier calliper has the main scale least count of $1 \,mm$. On the Vernier scale, there are $10$ equal divisions and they match with $11$ main scale divisions. Then, the least count of the Vernier calliper is ……….. $mm$

The diameter of a spherical bob is measured using a vernier callipers. $9$ divisions of the main scale, in the vernier callipers, are equal to $10$ divisions of vernier scale. One main scale division is $1\, {mm}$. The main scale reading is $10\, {mm}$ and $8^{\text {th }}$ division of vernier scale was found to coincide exactly with one of the main scale division. If the given vernier callipers has positive zero error of $0.04\, {cm}$, then the radius of the bob is $…… \,\times 10^{-2} \,{cm}$

A screw gauge has least count of $0.01\, mm$ and there are $50$ divisions in its circular scale. The pitch of the screw gauge is $……..mm$

Which of the following is the most precise device for measuring length:

$(a)$ a vernier callipers with $20$ divisions on the sliding scale

$(b)$ a screw gauge of pitch $1\; mm$ and $100$ divisions on the circular scale

$(c)$ an optical instrument that can measure length to within a wavelength of light?