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

The diameter of a cylinder is measured using a vernier callipers with no zero error. It is found that the zero of the vernier scale lies between $5.10 \ cm$ and $5.15 \ cm$ of the main scale. The vernier scale has $50$ division equivalent to $2.45 \ cm$. The $24^{\text {th }}$ division of the vernier scale exactly coincides with one of the main scale divisions. The diameter of the cylinder is :

In a vernier calliper, when both jaws touch each other, zero of the vernier scale shifts towards left and its $4^{\text {th }}$ division coincides exactly with a certain division on main scale. If $50$ vernier scale divisions equal to $49$ main scale divisions and zero error in the instrument is $0.04 \mathrm{~mm}$ then how many main scale divisions are there in $1 \mathrm{~cm}$ ?

$N$ 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 student measures the thickness of a human hair by looking at it through a microscope of magnification $100$. He makes $20$ observations and finds that the average width of the hair in the field of view of the microscope is $3.5 \;mm$. What is the estimate on the thickness(in $mm$) of hair ?