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

Student $A$ and Student $B$ used two screw gauges of equal pitch and $100$ equal circular divisions to measure the radius of a given wire. The actual value of the radius of the wire is $0.322\, {cm}$. The absolute value of the difference between the final circular scale readings observed by the students $A$ and $B$ is .... .

[Figure shows position of reference $'O'$ when jaws of screw gauge are closed]

Given pitch $=0.1 \,{cm}$.

If in a Vernier callipers $10 \,VSD$ coincides with $8 \,MSD$, then the least count of Vernier calliper is ............ $m$  [given $1 \,MSD =1 \,mm ]$

The circular scale of a micrometer has $200$ divisions and pitch of $2\,mm$ . Find the measured value of thickness of a thin sheet .......... $mm$

Answer the following :

$(a)$ You are given a thread and a metre scale. How will you estimate the diameter of the thread ?

$(b)$ A screw gauge has a pitch of $1.0\; mm$ and $200$ divisions on the circular scale. Do you think it is possible to increase the accuracy of the screw gauge arbitrarily by increasing the number of divisions on the circular scale ?

$(c)$ The mean diameter of a thin brass rod is to be measured by vernier callipers. Why is a set of $100$ measurements of the diameter expected to yield a more reliable estimate than a set of $5$ measurements only ?